What name did the Elvenking give to Bilbo?

The Elvenking did not give Bilbo a name. He was simply known as "The Burglar" or "Thieves" by the Elves of Mirkwood.

It was Thranduil, the Elvenking's son, who gave Bilbo the title of "Burglar of the Shire" after he escaped Mirkwood and was captured by the Wood-elves.