One easy way would be naming the Companion button with the variable:
$(QLab FB:q_BLAH_name)
$(INSTANCENAME:q_{num}_name)
Name of the QLab cue number {num}. See below for certain restrictions. --->QLab allows almost any characters in a Cue Number. Some characters don't play well with OSC or Companion. Using '$', '(', or ')' in your Cue Number won't work if you want to use the q_{cue}_name variable or the 'q_bg' feedback.
So have the Companion button always get the name from cue BLAH (or whatever "number that doesn't have to be made up of numbers") in QLab, and then use OSC or a script.
OSC
/cue/BLAH/name "Hello There"
/cue/{cue_number}/name {string}If string is given, set the name of the specified cue to string. If not, return the name of the specified cue.
Script
tell application id "com.figure53.QLab.4" to tell front workspace
set the q name of cue "BLAH" to "Hi"
end tell
q name (text) : The name of the cue. Not unique.