When I go into a game that is just starting with the 50 second countdown, I sometimes go in with the wrong character that I want to play ("Dragon7350" for example). I change my name in the console and reconnect using the command "setname Dragon7350|changecharacter Arkos".

After this, I enter the game like normal... but seemingly as someone with only spectator permissions: I can't join the game, but I can watch. Reconnecting causes the same issue. To join back, I quit UT2004 completely and restart.

Is anyone else having this issue?

You don't need to reconnect if you change your name or character before the countdown is finished. If you change AFTER the "game start" THEN you will need to reconnect.