What's your take on using your cousin's name (their own name, not their child's name) for your own child?

I'm 37 weeks and we've been stuck at the same point trying to come up with a name for DS2 for months. Yesterday DH shared his top three names, and of those I'd say I have a clear favorite . . . but I'm hung up on the fact that I have two cousins with the same name. One I never see, but the other we see a few times a year. We're not super close but not estranged by any means either. Would it be weird to use his name for DS2? They would have different middle and last names. There is no reasonable alternative spelling/variation/nickname of the name.

We both come from large families (~30 first cousins between us) and neither of us care for unique names, so I don't think we'll suddenly discover any new options in the next few weeks. Maybe it's just too much to ask to agree on a name that hasn't been used by a family member already

Unfortunately, his top three and my top three don't overlap at all. He's vetoed one of mine, says another reminds him of an annoying coworker, and hasn't said much on the third (but I don't think he's too hot on it). I'm thinking of vetoing one of his top three, and I just don't like the other option as much as my cousin's name once you take the family thing out of the equation.