Whether the enlightment one called Gotama because of his mother name is Mahamaya Gotami?

So, Gotama means that the son of Gotami?

Yes we can say that. Also I have read that his gotra(his lineage name) was Gautama hence he was called Siddharth Gautama.

Gotama is a name used by the clan following the lineage of the family priest (purohita). This was the established custom in those days.