Under their own guidelines it's fine https://stackoverflow.com/legal/trademark-guidance

> Do name your application with something unique. Including one of the terms, "Stack" or "Exchange" or "Overflow" in your product name is generally okay.

It's a different enough product that I feel comfortable with it - Stack Overflow is only for programming while Answer Overflow is for all topics. Along with that Overflow is a pretty generic word and if you wanted to get super technical with it, the context I'm using the word in is "I have so many answers they're overflowing" while theirs is a reference to a programming term.

We'll see and I'm not a lawyer but given that their trademark guidelines allow it, I feel comfortable