Is there a common name for pop-up damage numbers, such as in RPGs?

Two different names I have commonly heard used are Combat text or damage text. Both are used fairly frequently and are interchangeable, though in my personal experience, I have heard damage text used more frequently. See links for examples of use in games. Combat text generally also includes things like status effects as well. Damage text is just "damage numbers", which as @badp mentioned is another phrase that can be used.

Generalized, the term I see and hear the most for these kinds of things is "floating" text. It can be more specific: Dragonrage's answer mentions combat text or damage text, but it isn't restricted to a combat scenario. Floating text is often used to contextualize numbers or short phrases by causing it to float near whatever it's meant to represent - damage floats off of or pops off of the damaged creature or character (or their hp bar); gained resources appear as +1's near your stock of that resource, the places you collected or delivered it, or both; a reminder on which button digs for treasure could rise from the earth as your character nears the big X on the ground.

Sometimes I think the floating text that "pops" up and then falls away should be called something else, since it doesn't exactly "float", but typically I still hear it called floating text, or it's replaced with a more specialized term like "damage indicator" or "pop-up reminder".