Our twin names don't "match," but I do think they make a "set." Well, they seem to fit well together, and there's an interplay of letters that I like, but it's subtle. So it's not a "set" in any sense beyond sibling names that (I think) fit together well. And structurally they have some letter similarity.
If my daughter had been a boy, we planned to name her Noel Patrick. So that still was a name we liked, although we also were considering Neil. We liked Lyle, too. And Linus. (And a bunch of other names, including Otis, but that one would have been toooooo close to our daughter's name so Otis was right out.) Then we found out we were expecting twins, and that they'd be same-sex since they shared a placenta. Eventually, we learned they were boys.
No, we didn't consider Noel and Neil. Or Lyle and Linus.
We did consider Anselm and Ambrose, but more for the feel of the names together than because they started with the same letter. That didn't feel too "matchy" for me because I'd often considered how nice it would be to have two boys named Anselm and Ambrose (I never could decide which name I liked better, and I actually like each name better when they are together!), but I was imagining just brothers with those names not necessarily twins.
Well, we got the twins and I could have had my Anselm and Ambrose but for whatever reason, it just never really felt that compelling.
For girls, we were considering Margaret and Audrey. Also some pairs using Lilah. My favorite girl name was Willa, and my husband was lobbying for Veronica, so I was considering names that would go well with the nickname Ronnie. (He also liked Bernadette. We wouldn't have done Bernie and Ronnie, though!)
We ended up with Noel and Linus.