He's way too far down the line for it to matter at all about being a properly 'royal' name. Like, one day his uncle will be king? So let's look at the Queen's niece and nephew? Most people have no idea who they are. Princess Margaret's children are called David and Sarah. Perfectly nice, non-royal names from about 60 years ago.
What about Charles's nieces and nephews? Peter, Zara, Beatrice, Eugenie, James, Louise. There's nothing special about any of them. Only James is the name of former monarchs, but honestly, I can't see us having another King James after what happened to James II. Yes, there were princesses with the girls' names (not Zara, obviously), but when Beatrice and Eugenie were announced that took a lot of scrambling for most of us to find out.
Archie's second cousins are called things like Savannah, Mia, Lena and Isla. Normal, non-royal names.
He's not been named a prince, and I suspect he won't ever be one. So, I think it's not at all surprising for him to have a name that's popular at the moment. What I do find a bit cringey, personally is the Harrison/Harry's son thing. But whatever, their choice, and I'm definitely glad they stuck with just one middle name.
On another (mostly American) forum I was reading, everyone was screeching that they should at least have called him Archer. Can you imagine? Ugh.
And also, apparently, some people think that because there is one actress with a Pakistani name that is shortened to Archie as a nickname, this is somehow a "gender-fluid" (ugh, ugh, ugh) choice. Nope. That would be "unisex", but it isn't. It really isn't.