That vision of ancient religion portray sanctuaries dedicated to specific gods as independent religions, and that was not the case. The religion was mostly organized on a civic level, and there were sometimes priests who officed in multiple temples simultaneously. Of course during an invocation, ( at least in the archaic form of the greek religion) you would probably talk more about the good thing the deity did. You could look at the Homeric hymns (wich were not written by Homer by the way) to the different gods to see for yourself.