If Ronnie quit “Dio” what would they call themselves? And who would replace him?
Satan? You know, satan!
Peace,
mangeorge
You rang?
Well, it happened at least once before that a band named after one of its members would lose said member and stick it out (so to speak) without him.
The band was the Vinnie Vincent Invasion, named after an erstwhile ex-Kiss guitarist. One of his reasons for being ousted from Kiss was that he was supposedly an asshole.
Anyway, after two albums on Chrysalis, the members of this Invasion had a mutiny. They agreed that he was, indeed, an asshole. The remainder of the group stayed together and formed Slaughter.
Named, not for some violent allegory to the times we live in, but for Mark Slaughter, the band’s vocalist.
There are probably other examples of this (and no doubt better bands to use as examples) but the answer to your question as to what Dio would be called without Dio?
Anything those former members wanted to. Of course at this time there are so many former Dio players, I lose count…
Yer pal,
Satan
You rang?
Satan
Yeah, you. You up to the job? Maybe a little young, but they could use some fresh blood. 
Peace,
mangeorge
if they wern’t dio… they’d have to be called Scorpions… … or wait… yes thats it, the newest Black Sabbath concotion.
The wisest man I ever knew taught me something I never forgot. And although I never forgot it, I never quite memorized it either. So what I’m left with is the memory of having learned
something very wise that I can’t quite remember. -George Carlin
mangeorge:
If you are implying I should join the group, I must sadly decline. While I can offer the members of Dio a (much) younger presence, alas I cannot sing a note.
(Before people who do not know make some joke about how, as a metal singer, neither could Dio, I suggest you tred elsewhere. Dude got pipes. Even people who find him to be an arrogant and jealous of Ozzy for no damn reason little dwarf admit this much.)
If, mangeorge, you are suggesting they name th3e band Satan, it has already been done. I have their albium Court In Act and it’s really good for early '80s underground metal. Very fast, screaming vocalist, poor production, but worty of seeking out if you’re into that sory of thing.
“poor production,”
Sometimes that’s a plus.
Dio does, indeed, got pipes.
Peace,
mangeorge
I can think of a few bands that carried on without the member(s) for whom the band was named.
Good example: Fleetwood Mac. The band was named after drummer Mick Fleetwood and bassist John MacVie. But in the 70s, some of the band’s members broke away, and began recording/touring under the name Fleetwood Mac. Eventually, Mick & John had their day in court, and were able to put an end to that band. Today, they have exclusive rights to the name. Still, when most people think of Fleetwood Mac, they think of Stevie Nicks and Lindsay Buckingham, NOT the rhythm section. Regardless of legality, if Nicks & Buckingham formed a band and called themselves Fleetwood Mac, THEY’D get most of the band’s fans, not Mick & John.
In some cases, the musician a rock group is named after is NOT the real leader or focal point of the band. Spencer Davis was not the real heart of the Spencer Davis Group- Steve & Muff Winwood were. Jerome Geils was never the real leader of the J. Geils Band- Peter Wolf and (later) Seth Justman were. Now, Ronnie James Dio WAS Dio, for all practical purposes, so it would make no sense for his bandmates to try to carry on using the name Dio. But I think the J. Geils Band could continue to prosper without J. Geils, while Mark Lindsay could probably make a go of “Paul Revere & the Raiders” without Paul Revere.
Beyond that, even though most of the big band leadrs of the 30s and 40s are dead, bands using their name continue to tour, record and perform. Count Basie and Duke Ellington are long gone, but the Count Basie Orchestra still performs.
If Dio left Dio his logical replacement would be Sammy Hagar. It worked for Van Halen for a good ten years.
The Grateful aren’t, now that Jerry’s Dead.
Can I be Garth Brooks now? He seems to have left his own band.