My math teacher always called it a "hat" - I prefer that to caret. In math, caret or "hat" can denote an exponent - (example 3^2 where 3 is being squared). It's also used as a proofreading mark that shows where a correction or insertion of a new word should go.
Example... I like burgers.
^
veggie
It also has various meanings for computer programming languages, but I'm not sure about those.
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