As Melanie eluded to, stickers typically use a profile function (parser function / magic word) to automatically include the names in the template as documented in the profile fields for First Name, Last Name at Birth, Current Last Name, Suffix, etc.
In the event a sticker has custom text options available, you can change the output some, but for others, the text is hard coded and cannot be tweaked. In this specific case, I think the template in question is the Notables Sticker, which is one of the stickers that does not accept custom text.
I would also argue that even though her stage name may be the most recognizable, most users may actually want to see the "real name" in associated templates (genealogy and all that).
Stage names could also be applied to Authors in a form (nom de plume / pen name / pseudonym) and could get very tricky in the long run (e.g., Dean Koontz is recognized to have at least ten (10) pen names). As long as the stage name is covered in the Bio and profile fields in some form, the profile can be found through internal and external searches.