Why “Rama” Nama is called Taraka mantra?
By Taraka Mantra we basically mean the Pranavam, the first sound or OM, also called the Nada Brahman.
So, Taraka: Deliverer.
Taraka Mantra: From the root word tara–that which crosses. The Taraka Mantra is that which enables its invokers to cross over the ocean of samsara and attain liberation.
Taraka Nama: The Delivering Name; Om
From Sannyasa Upanishad:
That which is Om is the indestructible, the supreme and Brahman. That alone should be worshipped. It is this that is of the eight subtle syllables. And this becomes eight, being of eight forms. ‘A’ is the first letter; ‘U’ is the second; ‘M’ is the third; Bindu is the fourth; Nada is the fifth; Kala is the sixth; Kalatita (that beyond Kala) is the seventh; and that which is beyond these is the eighth. It is called Taraka, because it enables one to cross this mundane existence. Know that Taraka alone is Brahman and it alone should be worshipped”.
- When confronted with a mass of sins (i.e. when the flesh becomes weak, over-ruling the dictates of wisdom) he shall practise the (meaningful) repetition of the Taraka (Om) twelve thousand times (a day); for it cuts (sins).
Now, it's mentioned in the Vedas themselves (viz in Sri Rudram) that Lord Rudra liberates.
Namas taraya cha (prostrations to one who liberates)
And, it's also mentioned that Lord Shiva (or Rudra) is but Om in the Mantric level.
"atha kasmAduchyata o~NkAro yasmAduchchAryamANa eva prANAnUrdhvamutkrAmayati tasmAduchyate o~NkAraH "
Rudra is called the personification of Pranva because he sends the souls towards heaven, at the time of death (dissolution)
AtharvaSiras Upanishad 3.07
atha kasmAduchyate praNavaH yasmAduchchAryamANa eva R^igyajuHsAmAtharvA~Ngirasa.n brahma brAhmaNebhyaH praNAmayati nAmayati cha tasmAduchyate praNavaH||
He is called the “one who has the shape of Pranava“, because the Brahmins read and propagate the Rik, Yajur, Sama and Atharva Vedas only after reading 'OM
AtharvaSiras Upanishad 3.08
"atha kasmAduchyate tAra.n yasmAduchchAramANa eva garbhajanmavyAdhijarAmaraNasa.nsAramahAbhayAttArayati trAyate cha tasmAduchyate tAram.h "
He is called “Tara (Taraka - Liberator)” because he protects one from the fear of life which consists of the fear of staying in the womb, fear at time of birth, fear from diseases, fear from old age and fear from death"
Quoted the above verses from this page which basically discusses the same question as you are doing.
Same thing is stated in Puranas like Linga and Shiva.
“Ishwara [the Lord] said: O dear sons, recite this Om mantra which is identical with Me. Your knowledge shall be stabilized.” (Shiva Purana, Vidyeshwara Samhita 10:32, 33)
So, when Lord Shiva himself is the liberator and his Mantric representation is Om or the Taraka why would he need any other Mantra or names?
Also, in Kashi Lord Shiva liberates the dead. This is bodiless liberation as opposed to Jivanmukti, where one attains liberation while living. And, the following passage states that bodiless liberation is attained by OM.
Brahma asked: "Lord, what sort of a thing is the Brahman- OM?" 13 Narayana replied: "The Brahman-OM consists of sixteen morae [NpU 208]. It is within the range of the four quadruple states, since while awake there exist the four states beginning with the state of waking, while dreaming there exist the four states beginning with dreaming, in deep sleep there exist the four states beginning with deep sleep, and in the fourth there exist the four states beginning with the fourth [NpU 190 - 191, n. 84].  In the state of waking there exist the four forms of Visva: Visva-Visva, Visva-Taijasa, Visva-Prajfia, and Visva-Fourth.14 In the state of dream there exist the four forms of Taijasa: Taijasa-Visva, Taijasa-Taijasa, Taijasa-Prajfia, and Taijasa-Fourth. In the state of deep sleep there exist the four forms of Prajna: Prajna-Visva, Prajfia-Taijasa, Prajna-Prajna, and Prajna-Fourth. In the fourth state there exist the four forms of the fourth: Fourth-Visva, Fourth-Taijasa, Fourth-Prajfia, and Fourth-Fourth. These reside respectively in the sixteen morae: the waking-Visva in the phoneme a, the waking-Taijasa in the phoneme u, the waking-Prajna in the phoneme m, the waking- Fourth in the half-rnora, the dreaming-Visva in bindu, the dreaming-Taijasa in nada, the dreaming-Prajna in kala, the dreaming-Fourth in kaldtita, the deep sleep-Visva in sdnti, the deep sleep-Taijasa in sdntyatita, the deep sleep-Prajna in unmam, the deep sleep-Fourth in manonmam, the Fourth-Vi^va in pun, the Fourth-Taijasa in madhyamd, the Fourth-Prajfia in pasyanti, and the Fourth-Fourth in para [NpU 208, n. 107].  The four morae of the waking state are portions of the phoneme a. The four morae of the dreaming state are portions of the pho- neme u. The four morae of the state of deep sleep are portions of the phoneme m. The four morae of the fourth state are portions of the half-mora. This indeed is the Brahman-OM. It should be worshipped by Paramahamsas, Turiyatitas, and Avadhutas. Through it alone Brahman is manifested. By means of it one attains bodiless liberation."
Paramhamsa ParivrAjaka Upanishad.
So, Taraka is indeed the OM.
Lord Brahma told them: “Sudharshana (the holy wheel of Lord Vishnu) is that great Chakra. On its middle is written, the Taraka mantra (OM) and also the single letter of Narasimha (Kshroum), on its six petals of the Sudarshana six letters (Sahasrara Hum Phat) are written, on its eight petals the eight letters (Om Namo Narayanaya).
Nrisimha Purva Tapaniya Upanishad.
Then from where did this idea crop up that Rama Nama is also Taraka?
The page linked above provides the following answer:
However I wouldn't dismiss the claims of Vaishnava friends as unreal. Since their claim is based on Rama Uttara tapini Upanishad verses where it is said that lord Shiva did chanting of Rama's name in kashi where becoming pleased with him Rama appeared and gave a boon saying whosoever gets the "shadakshari" (six lettered mantra) from Shiva (in ears) while dying would get liberated.. Vaishnava friends need to grasp the Tatwam behind that story instead of reading it as it is. P.R. Ramachander who translated the Rama Tapini Upanishad has incorrectly mentioned the Shadakshari (Six letterred mantra) as "Ram Ramaya Namah". The sanskrit version of the upanishad doesn't mention this mantra at all. The upanishad mentions the following thing about the Shadakshara which is TARAKA.
"atha hainaM bhaaradvaajaH paprachchha yaaj~navalkya.n ki.n taaraka.n ki.n taarayatiiti " (Ramatapini Upanishad-Poorvopanishat 6.2).
"Sage Bharadwaja enquired Yajnyavalkya - 'What is Taraka? What is the one which liberates?"
"akaaraH prathamaaksharo bhavati ukaarodvitiiyaaksharo bhavati. makaarastR^itiiyaaksharo bhavati. ardhamaatrashchaturthaaksharo bhavati binduH pa~nchamaaksharo bhavati naadaH shhashhThaaksharo bhavati . taarakatvaattaarako bhavati. tadeva taarakaM brahma tva.n viddhi . tadevopaasitavyamiti j~neyam.h . garbhajanmajaraamaraNasa.nsaaramahadbhayaatsa.ntaarayatiiti . tasmaaduchyate shhaDakshara.n taarakamiti . . ya etattaarakaM brahma braahmaNo nityamadhiite . sa paapmaana.n tarati . sa mR^ityu.n tarati . sa brahmahatyaa.n tarati . sa bhruuNahatyaa.n tarati. sa sa.nsaara.n tarati . sa sarva.n tarati . so.avimuktamaashrito bhavati . sa mahaanbhavati . so.amR^itatva.n cha gachchhati " (Ramatapini Upanishad-Poorvopanishat 6.2)
"That which has 'A' as the first syllable, 'U' as the second syllable, 'M' the third syllable, half-note is the fourth syllable, dot is the fifth syllable, and sound is the sixth syllable; that is called the Taraka. That when practiced liberates one from the cycles of births and deaths. This is verily the ' Shadakshara (Six letered)' Taraka mantra namely Omkara. That person who regularly utters this Mantra, he gets ferried from sins, he gets ferried from death, he gets absolved of the sins like Brahmahatya (killing of brahmana), killing of foetus, he gets ferried from the ocean of Samsaara, he gest liberated from everything, he becomes one with the Avimukta (Lord Shiva as the redeemer), he becomes great, he becomes immortal".
Hence it is clear that the Six-Lettered Mantra what Rama mentioned is OMKARA.
One reference, however, i got of Rama Brahma Taraka is from another minor Upanishad called Rama Rahasya:
The great sages led by Sanaka asked Hanuman again, “Please tell us the mantra for meditating (or worshipping) the Taraka Brahma Rama.” Hanuman replied: 1. That king of mantra-s is the Ekakshara (one-syllabled) which is the store house of fire, which is Lord Vishnu who is lying down and which is Lord Shiva who adorned with the crescent moon. 2. Its sage is Brahma, meter is Gayatri, Deity is Lord Rama, its anga is waxing half-Moon and its mind is the soul of fire,
Rama Rahasya Upanishad.
Do scriptures mention any other names or mantras which can be used as Taraka mantra besides name of Rama and OM?
Yes, some other minor Upanishad mentions the Mantra "Om Namo Narayanaya" also as the Taraka.
Then Bharadvaja asked Yajnavalkya: “What is Taraka ? What is that which causes one to cross (this mundane existence)”. To which Yajnavalkya replied: “Om Namo Narayanaya is the Taraka.
Tara Sara Upanishad
Now, i have direct references from the Shiva Purana as regards which Mantra Lord Shiva whispers in the ears of the dead at Kashi in order to liberate them:
To understand the meaning of Pranava is to understand me. Pranava is the seed of all the lores.
It shall be understood as very subtle but possessed of great meaning even as the seed of the Banyan tree though very small contain» a huge tree. It is the initial mantra and the essence of the Vedas. Particularly it has me for its form.
- I am the the lord beyond attributes, the omniscenet and the omnipotent. I am Siva pervading ail but stationed in the single-syllabled mantra Om.
They say that whatever object there is whether synthesized into one or analysed in pieces is thc meaning of Pranava, thanks to the combination and importance of the attributes.
It is the imperishable Brahman, the means of attaining all objects. Siva creates universe at the outset saying "0m".
- Since there is not much difference bctwecn thc sense and the sound 0m, this is explained thus. Siva is Pranava or Pranava is Siva.
- The brahminical sages, the scholars who realize the identity between the sense and the sound know me as the single-syllabled 0m.
- Hence he who aspires for salvation and is free from aberration shall understand Pranava the cause of all and me as the Nirguna Paramesvara.
- O goddess, I shall give this crest-jewel of mantras at Käsi for the liberation of all Individual souls.
Lord Shiva's words to Goddess Parvati in Shiva Purana's 2nd Chapter of Kailasha Samhita (Translated by J.L.Shastri)
NOTE: The credit of finding these verses actually goes to The Destroyer :). I was unaware of them totally.
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