Can I name my baby
a) Youzarsif if i have a baby boy and
b) Adeeya if i have a baby girl?

Can you also please tell me the meaning of both the names. Adeeya means gift of god as per my knowldege. I am not sure about it so can you please tell me that its okay or not?

A) Yes, you can, but it has got no meaning to do so.
B) You mean Ateyya عطية, not Adeeya. Yes, you can.