The last time I used Western Union to send money (via the web site), I had to undergo a telephone security check and answer a series of questions to verify my identity and intent. In additional to the usual litany of personal information queries about past addresses and mother's maiden name though, this latest inquisition also included questions about a domain name I'd registered a few years ago.

Has anyone else experienced this or something like it? Are one's registered Internet domain names now also part of one's credit history?

It's part of public domain information. It is not associated with your credit history.