The rules say you shall not impersonate or falsely present. I think what that means is that you shouldn’t take measures that could convince a reasonable person to believe you’re someone else. Highlight on reasonable, convince and measures.
Simply saying “I’m your neighbors mum”, doesn’t mean I’m impersonating your neighbors mum.
I must try to imitate her in some way. Using a very similar name of char or corp, trying to convince you with “inside” knowledge and the likes. This is what impersonation means.
In other words: if a random stranger tells you he is someone you know in disguise, it’s your responsibility to check up on that. Not doing so is unreasonable. A reasonable person could not be convinced by such a mere statement, because they would always check back in some way.
If there is no somewhat objective reason a “normal” person could believe the lie, it’s not impersonation.
That’s why the OP won’t be successful with his petitions.