You can chant the ‘Rama’ mantra to any deity

 

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During Sivaratri, Abhisheka is done in all Siva temples. Why did Sri Sri Swamiji choose to perform Abhisheka to Lord Panduranga at Vittalapuram?

Sri Sri Muralidhara Swamiji:

It is believed that Lord Panduranga has the 'amsa' (divine aspects) of Lord Siva. Adi Sankara, in his 'Panduranga Ashtakam' ends every verse with the word 'lingam' signifying the same ('Parabrahma lingam Bhaje Pandurangam!')

In general, both Hanuman and Panduranga are considered to have 'Shiva amsa' in them.

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You can chant the 'Rama' mantra to any deity. In fact, Lord Siva Himself chants the 'Rama' mantra all the time. Hence you are absolutely right in chanting the Rama mantra.