Are you sure that you are not accidently double-selecting the band?
If you do, then the object handles are Grey, and you cannot edit.
If you only single select then the object handles are Green and you can edit
the text.
I do single click. It brings up a text box the same size as the whole band
and anything I type lands in the middle of the band. I am not allowed (or
can not figure out how) to rename the band its self.