For the first season, the boys last name remained "Jackson" and they called their Conrad Bain "Mr. Drummond." But later on, their last name is "Drummond" and they call Mr. Drummond "Dad." Was this change ever addressed in an episode?

Wish I could remember that detail, but I think that at some point they were going by "Jackson-Drummond" (it's written that way in the description of FOL ep # 14- "The New Girl"- see ep guide). Can anyone confirm this?

I think Willis and Arnold switched from calling him "Mr. D" to "Dad" after Drummond legally adopted them in Season 2 (episodes 31 and 32).
And I'm pretty sure they didn't change their names to "Drummond" until Season 7 (episode 164), when they did so as a birthday gift to Mr. D.

They never changed their names to Drummond. They did consider it in season 7, as the above poster mentioned, as a birthday gift to Mr. D. But Willis had seconds thoughts about his father's legacy, and Mr. D. let him off the hook.

Check out the initials that are on the boys' cabinets in their bedrooms. They still say AJ and WJ until Sam moves in, when the intials change to AJ and SM.