Just yesterday I retired my first king and had no idea I had to write the heir's name in the rename box or his name would stay the same as the previous king's. I just assumed since my heir had a his own custom name that the system would automatically change it.
I would like to suggest adding some sort of reminder or text stating that you have to rename the new king in the retirement screen or the name would stay the same as the previous king's name to prevent more players from making the same mistake I did. I feel that this is important as you have to spend GBs to change your king's name once it's set.