Basically expanding them more than just common time for 4/4 and cut time for 2/2, so far I have:
2/2 - Cut time (Ȼ), still in use
2/4 - Ordinaire time (O), comes from ”ordinaire” which is French for ”common”, because 2/4 used to be “French common time”
3/4 - Waltz time (W), comes from most 3/4 music sounding “waltz-y”, used to be grouped with common and cut time, but fell out of use
4/4 - Conmon time (C), still in use
5/4 (3+2) - Brubeck time (B), named after Dave Brubeck, composer of Take Five, the most popular jazz piece - if not music piece in general - in 5/4 - u/Barry_Sachs for the suggestion
7/4 (2+2+3) - Gabriel time (G), named after Peter Gabriel, composer of Solsbury Hill, one of the most popular mainstream songs to use 7/4 2+2+3
9/4 (3+3+3) - Zarabanda time (Z), comes from ”Zarabanda”, Spanish for Sarabande, a Spanish dance mostly written in 3+3+3 9/4 - u/victotronics for the suggestion
6/8 - Viennese time (V), comes from Viennese Waltz, a form of ballroom dancing with music in a fast 3/4 meter that sounded like 6/8 - u/MagicWolfEye for the suggestion
9/8 (2+2+2+3) - Rebetiko time (P), comes from Rebetiko, a Greek dance mostly written in 2+2+2+3 9/8 - u/victotronics for the suggestion (symbol comes from “P” or “Rho”, the Greek equivalent of the English R)
9/8 (2+2+3+2) - Tamzara time (T), comes from Tamzara, an Armenian dance mostly written in 2+2+3+2 9/8 - u/victotronics for the suggestion
10/8 (3+2+2+3) Jurjuna time (J), comes from Curcuna (also called Jurjuna), an Armenian dance mostly written in 3+2+2+3 10/8 - u/victotronics for the suggestion
12/8 - Sicilian time (S), comes from Siciliana music mostly being in 12/8 - u/victotronics for the suggestion