You could use straddle for cowgirl_position (then again, why wouldn't you be?) but all straddle tells you is a character is straddling something. There is a massive difference between "straddling something" and "straddling a person's crotch and facing towards their head while getting fucked by them". What if they are straddling a person's crotch and facing towards their head without getting fucked? There are no "facing forward" or "straddling person" or "on crotch" tags as far as I know.
Also, missionary position doesn't require you to be "on" your partner.
Updated by anonymous