I am sure lots of people have run into this problem many times in the past. That is when you have bids up in auctions or most especially rental items or loaned items out. You can't change the name of the character they are assigned to or retire them or do anything of that sort with them.
What I am proposing is to have just a rented item block or something that could potentially show what item it is exactly. This placeholder essentially would a couple purposes. First it would help show how many rental items you actually have out and on a specific character. Also you would be able to move those place holders around to new characters so that you could retire or Rename the first character if needed. One big reason this can be a problem is namely if you have month long rentals out. You would otherwise have to wait for as much as 2 months if they haven't even been rented out yet.