First of all your question is not that clear.But inspite of that let me try to answer it.Let's hope that it clears some of your doubts.
Who resides in our heart is your first question.So,let me answer that first.
Let's take the Sanyasa Suktam from the MahaNarayanopanishad as found here .Quoting from the last two verses :
Dahraṁ vipāpaṁ parameśmabhūtaṁ
Yatpuṇḍarīkaṁ puramadhya saggaṁstham |
Tatrāpi dahraṁ gaganaṁ viśoka
Stasmin yadantasta-dupāsitavyam |3|
Yo vedādau svaraḥ prokto
Vedānte ca pratiṣṭitaḥ |
Tasya prakṛati līnasya
Yaḥ parassa maheśvaraḥ |4|
Meaning-In the citadel of the body there is the small sinless & pure lotus of the heart which is the residence of the Supreme Person.Further in the interior of this small area there is the sorrowless ether.This is to be meditated upon continually. |3|
He is Maheswaraha(Lord Shiva) who transcends the syllable OM which is uttered at the commencement of the recital of the Vedas which is well established in the Upanishads & which alone remains after the final dissolution.|4|
So,according to Sanyasa Suktam Lord Shiva(Maheswarah) resides in our heart.
and who is the object of meditation of the Sanyasis.
Now, if you read the Narayana Suktam it also says almost the same thing in a slightly different way.
So,i have quoted from the most authoritative scriptures ,the Vedas, to show what it says about who resides in our heart.Its basically God who resides in it,& who is one but we know Him by different names.
So ,you can say that Shiva resides or Narayana resides ,the meaning both being just the same.
Now, coming to your second question regarding who first emphasized the glory of Rama Nama.
It was Lord Shiva.
Quoting from this page:
The Vishnu Sahasranam is found in the Mahabharatha. Literally
translated this means thousand names of Vishnu. This is found in the
Anushasanika Parvam (chapter relating to orders or rules to the kings)
of Mahabharatha. ......... In the afterward to the stotra Goddess
Parvathi asks Siva the cosmic god for an easy way to sing this stotra
for the learned. He replies that it is sufficient that the learned
one repeats the name of Rama and this is equivalent to his singing of
sahasranama. It is important to note that this is easy method is
prescribed to the very learned who do not have time to recite it daily
and not for everybody,
The greatness of Rama Nama is also described in the Bhavisya Purana as follows:
Rama namahi tat jnyeyam Sarvaaghouga vinashanam (Rama nama itself
would destrory all the sins).