It doesn't spell disbandment per se, but you better believe that group isn't going to be very active from that point on. If you ask for a solo fandom name, you consider yourself a solo artist first & foremost.
Display MoreYes, Taeyeon has a fandom name, every SNSD member has.
Taeyeon – Taeganger
Jessica – GorJESS Spazzer
Hyoyeon – Hyohunnie
Yuri – Yurisistable
Tiffany – Fanytastic
Sooyoung – SooYoungster
Sunny – SunShiner
Yoona – YoonAddict
Seohyun – SeoMate
No, it doesn't have to do with disbandment. Most group members has their own fandom names, even if they're still together.
Here's a list I find for some groups and soloists.
Most of these are unofficial, fan-created names.