Here is the way the whole story after the plowing of Denmark by Gefjun is summarized in another work by Snorri Struluson, the Ynglinga Saga:
Now when Odin heard that things were in a prosperous condition in the land to the east beside Gylve; he went thither, and Gylve made a peace with him, for Gylve thought he had no strength to oppose the people of Asaland. Odin and Gylve had many tricks and enchantments against each other; but the Asaland people had always the superiority.
In Gylfaginning, it is also said that the reason Gylfe is trying to go to Asgard is to learn about the source of the power of the Ases:
King Gylfe was a wise man and skilled in the black art. He wondered much that the asa-folk was so mighty in knowledge, that all things went after their will. He thought to himself whether this could come from their own nature, or whether the cause must be sought for among the gods whom they worshiped. He therefore undertook a journey to Asgard. He went secretly, having assumed the likeness of an old man, and striving thus to disguise himself.
So, my understanding is that Gylfe motive is revenge: he was just tricked by an Asa (Gefjun) into losing a big chunk of his kingdom, he knows that the Ases are too powerful for him to fight, and tries therefore to learn a little about them to spot weaknesses.
So naturally when he sneaks into Asgard for that purpose, he tries to hide his identity.