I suppose the definition of intentional is a bit murky here.

Yeah, you're right that Google probably didn't look at a list of open web technologies that they disagree with and choose one for their new tool. I guess I'll call that "malicious intention".

I'm sure that, however the name was picked, Google's lawyers looked for prior uses of the name. I'm sure it came up, and Google shrugged its shoulders in indifference. Maybe someone brought up the fact this would hurt some open standard or whatever, but nobody in power cared. Is this the same kind of malicious? Probably not, but it still shows that Google doesn't care about the open web and the collateral damage they cause.

surely the lawyers found far more name clashes with Bard than Gemini

https://books.google.com/ngrams/graph?content=gemini%2Cbard&...

Have you ever tried to name something? Anything that isn’t an outright racial slur is in use by something. Usually dozens or hundreds of things. Some protocol that almost no one has even heard of is going to be very low on the list of conflicts to avoid. This has nothing to do with the open web.

Gemini? You mean the name used by Gemini Data Inc 8 years before the Gemini protocol was launched?