Ideally it would be nice to change them on the fly, example, I work at a webhosting company where we have a central server we connect to and then for security purposes only it has SSH access to the other nodes, etc.. so being able to go in and label one tab "ams-node12" with another "mtl-node3", etc.. this lets me know what I am connected to, and since in that type of setup we cannot simply make an SSH connection for reach server since it's locked down, which given my history in the industry is pretty standard.

+1 this, I am not a fan of auto-save either for similar reasons, document tab should have * prepended until manually saved if Auto-Save is disabled.