Cite? From what I see that ceases being true by about age 30 for the vast majority of people.
No, you've got that backwards. Millenials don't give a shit about cars. But IME the majority of people who give their cars names are over thirty and female, or over fifty and male.
You've changed your claim. You're now discussing not the majority of people but the majority of people who name their cars which as far as I can tell is a very, very small percentage of automobile owners. I find it believable that people who name their cars wouldn't like to rent one. Note that that's not the same as saying I believe it.
Your claim about ages rings hollow to me, though. I don't know anyone over the age of 25 who has named their car. Of course, I only know two people who have named their cars, period (one is 21 and one is 19).
However, my experience doesn't really matter. You're the one making the claim that no one will be willing to buy a car that doesn't perfectly fit all of their needs, so it's on you to support it, not on me to refute it.