Actually, I suppose a name being used for a drug or a Pokémon precludes it from being used for the other, so it is a very shared issue, lol.
Theoretically, unrelated trademarks can have the exact same name in different fields, owned by completely different owners, but that generally only applies to trademarks that are regular words that are already in use: Apple Computer versus Apple Music (which the Beatles owned and ended up selling to Apple Computer), Monster Energy Drink versus Monster Cable versus Monster Jobs, Dove soap versus Dove chocolate, etc.
Still, the law looks to likelihood of customer confusion, and maybe it would be too confusing to have a Pokemon named Ozempic.
Theoretically, unrelated trademarks can have the exact same name in different fields, owned by completely different owners, but that generally only applies to trademarks that are regular words that are already in use: Apple Computer versus Apple Music (which the Beatles owned and ended up selling to Apple Computer), Monster Energy Drink versus Monster Cable versus Monster Jobs, Dove soap versus Dove chocolate, etc.
Still, the law looks to likelihood of customer confusion, and maybe it would be too confusing to have a Pokemon named Ozempic.