This was inspired by this question: Should I allow players to recreate the exact same character if they die?
Whilst it was closed as too subjective (because it asks whether one should want to do this), I think there was an interesting subject matter here, so I'm going to start my question with the premise that I do want to discourage my players from doing this.
As for whether or not I should feel this way, I believe the answers to the other question already cover that (basically, is the rest of the table as troubled by this or is it just me, and if it is just me then does it really matter if that's what the players find fun?).
However, if I need to justify my position, I personally find it boring and unimaginative and therefore it would take away from my fun to some degree if they just made the same character again after they die (especially since I try to work elements of the player's character's backstory into the game, so if the same character turned up with the same backstory, that would disappoint me). However, it doesn't take away from my fun so much that I want to stop DMing for these players or force them to make different characters.
So, to restate that last point, I don't want to force my players to make a new character; as some of the other question's answers have said, some players just like playing the same character (either literally, same name and backstory and everything, especially if they don't take character death well, or more broadly the same character, such as someone who always makes a dwarf fighter with roughly the same personality but with a different name and a slight variation to their backstory), in which case there probably isn't an answer to this question that wouldn't also reduce their fun. Hence this question isn't about those players who won't budge, it's about players who aren't quite so determined to make the same character over and over, but might do so anyway.
So, to try to keep this within the limits of "Good Subjective", my question is: what methods have you personally used or seen that successfully encouraged players to make new characters or discouraged them from making the same character without forcing the players into it?
I imagine most answers will be answering from the perspective of the DM, but if someone has achieved this as a player, influencing another player to make a different character (without forcing them), then such answers are also welcome.