From a mans point of few I can tell you that insecurity is very unattractive. You can share that you don’t like it but don’t show insecurity about it and don’t nag.
On the other side that car arrangement sound pretty shaky. If he is paying why on Earth would it be in the ex-girlfriends name. Unless he owes her money and she doesn’t trust that he will pay if it is in his name. Can she be trusted???