Anheuser-Busch InBev NV has a plan to make America great again—or at least sell more beer.

The nation’s largest brewer is stamping the word America on beer cans and bottles that would usually say Budweiser. The packaging also substitutes “US” in the logo’s crest that would usually say “AB” and drops “King of Beers” for “E Pluribus Unum.”

The...