Laura: So, you're okay with your snacking now?
Adam: I've accepted it. Fish gotta swim, you know? Birds gotta fly.
Laura: And you...have to eat bite-sized snack food?
Adam: Adams gotta cheez-it.
Laura: Lauras gotta cocktail.
It’s not plural – there is only one Adam, and only one Laura. It’s not possessive, either, as they are describing what they need to do, not something they own. It’s actually a contraction, combing the verb “has” onto their names, and therefore it should have an apostrophe. “Adam has gotta (eat) Cheeze-its”. “Laura has gotta (drink a) cocktail”.
It’s not plural – there is only one Adam, and only one Laura. It’s not possessive, either, as they are describing what they need to do, not something they own. It’s actually a contraction, combing the verb “has” onto their names, and therefore it should have an apostrophe. “Adam has gotta (eat) Cheeze-its”. “Laura has gotta (drink a) cocktail”.