Does anyone know the name of the ae combined symbol in Latin?

It's a grapheme of A and E.

As a letter of the Old English alphabet, it was called æsc ‘ash tree' , but in modern English, it's just referred to as "ash"

Ae Symbol

"ash" is correct. Or more fully the "ash ligature". (A ligature is the name for two or more letters combined to form a single character.)

Another ligature you sometimes see in English isœ (o + e), called the "ethel" (which you might find in a word like "onomatopoeia").

Funny thing is I didn't learn about "ligatures" in English class (though I'd seen a few), but from reading German, where in place of a double-s at the end of a word you might see the ligature ß

I have no quarrel with the previous answer. On my computer one can print æ by holding down the Option key and striking the apostrophe (').

Diphthong.