Because the name Ram is the divine, the eternal Brahman, it is Taraak Mantra.
But How ?
Let's see how Rama is the name of the whole past world.
There are 3 characters in the word Ram - R, A and M. According to the Pulha Samhita, there is the origin of Brahma, Vishnu, Shiva, with the Character R named Rama.
Example - One name of Brahma ji is Birchchi, a name of Lord Vishnu is Lord Hari and Lord Shiva is also known as Shankar.
There is Character R in Birchchi, there is Character R in Hari and there is also Character R in Shankar. It became certified that Brahma, Vishnu, Shiva appear with the Character R named Ram.
Similarly, there is the origin of the trinity of the name Ram.
Examples - Uma, Rama and Brahmaani. These three are the names of mother Parvati, Lakshmi and Saraswati respectively.
Uma has Character M, Rama has Character M and there is also Character M in Brahmaani. So it became certified that three goddess appear in the name of Ram in the Character M.
Now remains is the Character A between the name Ram.
Lord Vishnu says in the duality of Bhagavad Gita that "O Arjun, I am a Character A in the letters."
In the Rig Veda, the first spell is of fire, Agni is also a symbol of Character A. That is, the Character A which is the letter is Brahma.
That is why the letter which is between the name of Ram is itself in the form of God, the letter Brahma. Similarly, the name of the Ram named Ram is the reader of the Trinity and the master is the reader of the Trinity.
Overall, We can say that there is nothing beyond the name of Ram in our Vedas. There is nothing beyond Character R, Character A, Character M with whom Ram is named. You take any mantra, there will be Character R, Character A, Character M will be there. So there is nothing beyond these 3 sounds and this 3 sounds together make a Ram name which is the best mantra.
Regarding being called Lord Shiva's Ram, it is the opinion of scholars that Lord Shiva has chanted Ram Mantra by churning out all Vedas, Puranas and Shastras. On the name of this Ram, Lord Shiva liberates every creature while sacrificing life in Kashi, whose proof we find in Shri Ramcharitmanas -
Now you may be thinking that why is Lord Rama named Ram so dear?
"All the gods [from its part only] with the effect of the name of Ram, have become revered by the manifestation; this mystery is known to Mahesh Lord Shiva only, others do not know."
Lord Shiva says to Bhagwati Parvati:
"Oh Goddess Parvati! After listening to the names starting with character R, my heart is filled with love due to the name of Ram."