I recently labeled my mailbox with my name and asked my mail carrier not to deliver mail addressed to other people at my address (I live alone). I would also like to request my mail carrier not deliver mail addressed to "current resident," "occupant," etc. Is it illegal for my mail carrier to dispose of mail addressed to "current resident" if I request it?
Yes, it would be illegal: The mail carrier has to deliver mail to the address. But he should generally not put mail that doesn't match the name on the door in any mailboxes there. If someone doesn't live there and you accidentally get Jane Doe's mail, you have to make sure it is put back to the mail system so it can be returned or delivered correctly.
"Current Resident" however is addressed to you. As it is your home, you are the intended recipient, and you can not return that as not-the-addressee.