First thing to remember is that there can be more than one profile active at a time, which could complicate things. Also, there is currently no scripting variable that contains the currently active profile names.
Having said that, one way you could accomplish what you’re trying to do is to set each profile to manage the tagging scripts, and then add a script to each profile that sets the tag to the profile name. Something like:
$set(source,Picard profile name)