Both the boys have breezy nicknames that are ironic because their personalities are anything but easy-going. Willy hopes his boys will be "well-liked" and their names seem to indicate a familiarity in society that neither one possesses.
Biff is a failed football hero. He is disillusioned by his father's lack of success and lack of his own achievement. His child-like name is a reflection of his emotionally stunted growth. Instead of taking responsibility for his own failures, he blames his father for everything. Willy doesn't help raise him to a level of mature responsibility. He continues to see his son as potentially great instead of dealing with the reality of Biff's limitations (and his own.)
Happy, of course, is a highly ironic name for the character. Happy would more aptly be named Miserable. Happy has grown up hearing about the wonderfulness of his brother. He never impresses Willy the way Biff does, though like all children, he desperately wants his father's approval. On the surface, it seems like the name fits. He is handsome and charming, but a womanizer, constantly looking for validation and approval.