We currently have Dame Janet Baker in the database with her title (Dame). @spitzwegerich has entered edit #47877200 to remove the title. (We also have Sir Adrian Boult, but Edward Elgar without Sir. And no doubt plenty more.)
The style guidelines seem less useful than you’d hope here. They tell you things like “in most cases, it is the name as found on releases” which aren’t really useful for classical considering how different release will write people’s names completely differently, for stylistic and/or space reasons. The guidelines also say “honorary titles (like ‘Sir’ or ‘MBE’) if they’re actually used by the artist as part of its name.” Ignoring for a moment referring to her as an “it”, there are a bunch of release that do, and a bunch that don’t. That’s fully what you’d expect even if she does consistently consider it part of her name—just because the cover art designers shorten names all the time. We don’t question if artists consider their first name part of their name just because covers often only print the last name.
Seems like this guideline is more aimed at pop artists who consider their names & band names a brand, and care quite a bit about how it’s written.
Last thing, I’m not actually sure what renaming an artist does to existing credits. The ones crediting her as “Dame Janet Baker” don’t currently have a “credited as” (because they can’t; AFAIK the site won’t even let you put that in if you try). If we change the artist name, will those release now have incorrect credits? If so, that’d suggest if we have no strong feelings one way or the other to keep the status quo…
[edit: correction: The site will let you enter an AR credited as the same as the name; checked in https://musicbrainz.org/edit/47913541 … of course, I doubt anyone does that.]