In which Chinese topolect might 門 be transcribed as ? There's a Cantonese restaurant in Mountain View, CA called Fu Lam Mum -- the characters are clearly 富臨門.

But 門 has always had a -n final, in any topolect I know of, and back to MC and OC according to Baxter's reconstruction. Therefore this must be a sound change (assimilation at a distance) in a daughter language.

In what topolect, if any, does 門 have an -m final? Being a Cantonese restaurant in the US, I'd suspect Taishan, but that's just a guess.
I'd say it is a local Hongkong final consonant drift n->m, as 10300 Googool results for 屯门 (Tuenmun / Tuenmum) would indicate:

http://church.oursweb.net/church.php?pkey=816478 (Tuen Mum alliance church)

https://www.youtube.com/watch?v=CektDpGGXWQ (Light rail at Tuen Mum ferry pier)

https://zh-tw.facebook.com/ourinteriorsltd/photos/a.122323427797946.13546.122300641133558/122323507797938/ (Marina Garden, Tuen Mum)

http://johnblog.phychembio.com/?tag=tuen-mum屯門 (Tuen Mum(屯門) | John Chan Photography)

http://hkims.org/activities_Calendar.html (屯門共修 7 - 9pm Tuen Mum Group Sitting)

Sorry to say I do not speak Cantonese, but such drifts in consonants/wovels are not unheard of. Across East Asia, there is a certain mux between l/r, and Beijing vernacular has a spectacular w->v drift that is similar.