As far as I know, beyond some joking, there has been no discussion of changing the name or closing down this place. While LucasArts is no more, there will still be future Star Wars games and hopefully non-Star Wars LA franchise games. The recent years not withstanding, LucasArts had a rich history of producing some very memorable games over its life. No reason to act like it never happened just because Disney decided to go in a new direction. Most of us grew up playing and loving these games, Disney can not cannot cancel that.
Plus Lynk will not leave for us to turn out the lights.