It is a very beautiful and interesting poem. I am not an expert in Eastern philosopy but I think I understand what the poet is trying to say. Here is my interpretation.
The innermost one is the Supreme Consciousness, the One. The One is reality. It is he who creates the world of maya, the world of illusion, of names and forms, of me and you and they.The ego or self* separate from the One is another form of this illusion.
When the innermost one "lets peep out through the folds (of maya) his feet" he lets the truth of oneness be seen and experienced in a small way. Just the touch of his feet "at whose touch I forget *myself" removes the illusion of self and the poet feels the reality of the innermost One.
Days come and ages pass, .........time is another illusion--one day is no different than an age.
and it is ever he who moves my heart in many a name, ......it is always the innermost one, no matter what name you give him (God, the Universe, Allah, Supreme Consciousness, etc) touches the poet's real being (heart).
in many a guise...... the innermost one takes many forms....people, animals, objects, etc.
in many a rapture of joy and of sorrow.....the innermost makes himself known through many mystical experiences, sometimes taking the form of joy and sometimes sorrow.