Is it wrong to restrict naming conventions to be more original?

Been DMing for years and this has always mildly irked me about a few of my players, but not to the point of actually getting upset/arguing.

I have 6 players (wife, her three siblings and two of their SO, so all family) and when we make characters, a few of them don’t know how to come up with names for their PCs or pets.

One of them I helped make his entire character and said “okay, we just need to name him” he said “hmmm, idk.” Looked around and the first thing he saw was my dog (he loves my dog) and said “I’ll name him (my dogs name)” and I was like “no, pick something else. I’m not potentially narrating my dog getting stabbed and bleeding out or something like that.” I was overruled by the rest of the party as it being no big deal so I let it slide and now my wife gets sad when I say “(dog name) gets shot by an arrow.”

And another player who has made a total of 4 characters since we started playing across all our campaigns names every single one of them after a video game character that we all know and I ask for them to think of something original and they say:

“I can’t, I’m not good at it.”

Me: “use a generator or something.”

Player: “I looked and didn’t like any of them, they sound generic.”

Me: “isn’t stealing a name kind of generic?”

Player: “well I’m basing the design and vibe of the my PC off this character so I thought naming them that made sense anyways.”

And then I’m overruled as big dealing it and now all I think of is that PC being exactly that video game character in my/our world/game.

We are starting another campaign where I will finally not DM and a third players is naming her class pet after her dog and said it looks exactly like her irl dog, too. It irks me but I’m also not the DM so I have no control over it.

Edit: word