Bogmire has the distinction of being the only Portait Ghost to have a Lego!... okay uh I don't have much to say about him but I really do like Bogmires design! its the most Mario enemy Looking Potrait Ghost in the Game which I like :D
Okay, I have an incredible theory about Luigi's Mansion:
This guy
and this guy
are the same person.
(Theory under the cut cuz it's a long one)
So first, some background (which is basically a whole other, much bigger theory in and of itself). The portrait ghosts are distinct from almost every other ghost in not just Luigi's Mansion, but the whole expanded Mario universe, in that they're just straight-up ghosts of a sapient species (yeah, I know that Eeries and Ghost Guys are a thing, but they feel different). They're also all ghosts that E. Gadd collected, which brings up an interesting issue. He collected them from all over the world, and the mansion they all (un)live in appeared out of nowhere a few days before the game, and yet most of them have clear or implied connections to each other and the mansion seems to have a lot of their personal histories built into it.
Here's what I think is the solution to that issue. Vincent van Gore can paint ghosts into being, and all the portrait ghosts are, well, portraits. I believe that all of them are paintings of people who lived in the mansion at one point, including van Gore, who is a self-portrait (when all of the ghosts he summons in his fight are defeated, he says that only one of his creations remains, which lends some credence to this).
(Just because E. Gadd has a machine that turns ghosts into portraits doesn't mean they weren't already portraits at one point- it's possible he made the portrait machine by reverse-engineering their portraits or something)
"But wait," you say, "wasn't the mansion just created out of nowhere, like you said?". However, one of the portrait ghosts, Shivers the butler, gives a possible reason for the mansion to need to be created out of nowhere when it was already a place that existed: it simply burned down, which may even be how Shivers, and possibly a few other portrait ghosts, died.
So now we get into the actual "Vincent van Gore is Bogmire" part. I believe that, due to a few pieces of evidence, such as a painting of a living van Gore being front and center in the Parlor, van Gore is most likely the original owner of the mansion. This means that there's a good chance that his spirit would linger around the mansion- but the Vincent van Gore you encounter in-game is a self-portrait, not his actual ghost, as stated above.
Bogmire has some possible ties to van Gore, though. His grave is the biggest and oldest-looking in the graveyard, fitting for the original owner of the mansion, but more so than that is the fact that he's stated to be "a product of the mansion's fear and despair". How exactly would a product of the mansion's fear and despair have a grave? It never even would have been alive!
Essentially, I believe that Bogmire is Vincent van Gore's actual ghost, who absorbed the fear and despair created by all the misfortune that befell the future inhabitants of the mansion and evolved into the Bogmire we know and love over time. Meanwhile, the self-portrait van Gore painted portraits of all those inhabitants, imbuing pieces of their spirits in them as the original van Gore had with him and keeping them alive after death, in a sense.
So TL;DR: Vincent van Gore is a self-portrait of the real guy, Bogmire is the real guy's actual ghost after absorbing a bunch of bad vibes.
(Can you tell I'm hyperfixating on Luigi's Mansion just a bit rn)
