I have just learned that my metamour (who is gender queer and uses they/them pronouns) is switching to a chosen name rather than their given name. The name they have chosen is extremely similar to my name (the same four letters, just two letters are swapped places). It makes me kind of uncomfortable that our names are going to be so similar now and I think our shared partner feels a bit odd about it too. I really want to support their exploration of their gender identity and I know that a name one feels comfortable with is important, but it just makes me feel uneasy. Even as I write this it feels a bit petty, but I think it is compounded by the fact that we haven't had the best relationship for about a year and they have felt a lot of jealousy/insecurity about my relationship with our shared partner.
That definitely sounds like a weird situation, but my advice to you is to just try and let it go.
When people choose their name, especially as part of a transition or gender exploration, there’s usually a lot of soul searching and personal significance that goes into it. It’s highly unlikely that they chose that name as an attempt to bother you or influence your relationship with your shared partner. It very likely has absolutely nothing to do with you, and is just a coincidence.
In that case, if you Make A Deal Out Of This, then you’ll look petty and insecure, and it’ll be a bad look. There are only so many names out there in the world, and sometimes we have to share. (I had five - FIVE! - girls named Ashley in my first grade class.)
And if they did choose it in some part because of you, that’s their problem. I can’t imagine that such a choice would come from a healthy place, whether it’s jealousy or idolization or something, and I just feel bad for someone who is so emotionally stuck in issues around their metamour that they would choose a new name for themselves based on that. But even in that case, that’s really about them, and it doesn’t really affect you.
If that is the case, then if you Make A Deal Out Of This, you’ll only be giving them what they want. If this person is acting out of some weird power play or insecurity, other people will be able to see that pretty clearly, and you’ll only look extra gracious if you rise above it.
No matter what, the best thing you can do is just privately agree with your partner that it is a little odd, and then move on. I know plenty of polyamorous people who have partners with the same or similar names, and it’s actually very manageable. If someone else makes a comment about it, give it a shrug and a smile, and say that you appreciate their good taste in names as well as partners.