Thank you both. I deleted the account, and like mib2berlin says, Vivaldi Mail did give me the option to leave the read mail where it was. I was using POP3 for that account.
When I tried to make Runbox one of my accounts this time, it worked without any prompts. And I was able to add the original Comcast account - the one that then got saddled with the Runbox name - also without a problem.
This time, I established the Comcast accounts as IMAP. I had a traumatic experience with IMAP once, but that was about fifteen years ago, so maybe IMAP and I have both grown up since then. For now, it's all good.
I suppose the only mystery is why VMail assigned the Runbox name to an existing account. While I was setting up the accounts again today, I looked out for somewhere I could have gone wrong and couldn't identify anything at all. Unless somebody else reports it, maybe we could just call it a ghost in the machine.
Thanks again!