Yeah but let's face it, there's almost a 100% chance that Iommi was equally as influenced by not wanting to get on Sharon's bad side as everything you mentioned.
Then she sues him for 50% of the name a few years later anyway, claiming that it should actually belong equally to all the original members of Black Sabbath, settles the lawsuit, gets the original band back together and magically no one brings up the Osbourne's absurd statement about the name being equally owned by everyone, even as they can the drummer and turn the drum stool over to the stiffest and absolute worst Sabbath drummer in history, Tommy Clufetos.
BTW, there is a hilarious interview with the Sabbs, err, Heaven & Hellers on Eddie Trunk, I think the night of the big Radio City show. They discuss the name and Dio is hilarious. Geezer is drunk off his ass too. Ronnie says that they thought about naming themselves Tommy Miami and the Corvettes (or something even more hilarious) and then said, they also kicked around the idea of calling themselves Geezer Butler and the Italians. They talk about how to pronounce the name "Appice" and the normally reserved Geezer chimes in and says, "Everyone always gets my name wrong. It's actually BOOTLAH " and goes on and on as he gets drunker and drunker.
By the end of the night, Geezer was literally just making noises into the microphone.
I would pay someone several dollars if they could find that interview.