Whenever the leadoff batter gets on without an official AB (e.g. walk or HBP), the next batter is introduced as the leadoff batter.
I had my team name picked in DD as the Wolverines, picked Wolverines as my announcer name, and when the stadium announcer would say "next up for" or "leading off for" it would say "Guardians." Whenever it would say "next up for Michigan" it would be correct though.