Ganesha is known not by one name or two, but by many names, Each name has an explanation. Because of his elephant face he is called Gajanana ('Gaja' meaning 
elephant); as the leader of Shiva's Gana he is known as Gananayaka; he bestows boons on his devotees and so is Varasiddhi Vinayaka, he is Vidya Ganapati because he grants knowledge and wisdom; he is called Gowriputra because he was born by the grace of Parvati, Ekadanta because he has only one tusk, and Vighneshwara because he is the Lord of all obstacles - so he has many names.

The belief that, Ganapati loves his devotees immensely is the reason for his worship everywhere.