Sharon, you've been our "team leader" on Charlemagne for so long, no doubt you've already heard every possible "solution" to the naming problem.
My personal preferences are a bit different than yours, but my bottom line test for any profile and any solution is whether the information is actually wrong or whether it's just a question of presenting the same info in another way that something likes better. If the argument is just about personal preferences, I move on to more interesting topics ;)
One of the underlying problems here is that Charlemagne's and his grandfather Charles Martel's "real names" are unknown and probably unrecoverable.
They spoke a Germanic language so it must have been something close to Carl. I've seen the suggestion that it might have been Carol. There are two arguments for that. First, we know the normal way of Latinizing Germanic names was to add a -us ending. The Latin form of their name is Carolus, so it is plausible their name was Carol. Second, the modern Dutch form is Karel and the Old Dutch form is Carel. The Old Low Franconian language spoken by the Franks is thought to be the primary ancestor of modern Dutch, and Dutch is often used to reconstruct Old Low Franconian.
A related problem is both men lived their lives on a public stage in an "international" world where they governed people who spoke many different but related dialects. So, the idea of a "real name" is elusive. In the days before language and name standardization they probably would have identified with many variant forms of their name in a way that would not be possible for someone who lived later, after standardization.
As an aside, I wrote a college paper where I wanted to find some variant forms of Charlemagne's name from the Chansons de Geste (about 250 years later, and written in medieval French). I came up with Carle, Carlemagne, Carlemagnes, Carles, Carlon, Carlun, Charle, Charlun, Karle, Karlemagne, and Karlon). For Charles Martel, I have Karleh, which I think is what the Arabs called him. There were probably others but this list was enough for my purpose at the time. Taken together these are all indications of a dialectal variation around an unknown original.
This is all prep for a different topic. The point is that when we think about how to record Charles Martel and Charlemagne we can't fall back on the idea of real name. We don't know what it was.