Simply prohibit it
Is that easy for me to say? Maybe, but in the end that's all there really is in that. I could say … But I do not have many options in my area for players & # 39; or 'But this is my friend and I do not want to deny it & # 39; or & # 39; but this guy has some personal circumstances that make having the same character all the time comforting him & # 39; and all that is worth considering, however, at the same time, you are the GM , and it is up to you to manage (not control, this is a collaborative hobby) the fun of the game, so that is fun for both you and the players.
If you let the integrity of the game suffer in the long term to avoid short-term disagreements, you will lose more than just a small argument. Over time, that kind of thing weakens the whole game and in a short time you have given up too much, and people start finding other things to do with their time.
You are the DM. So I know the DM. Any new character requires their approval to exist in the game, and if a carbon copy of the previous one is not acceptable, that is all. If your players are simply crossing out the names and writing new names if your character dies, that is indicative of a more fundamental problem than the lack of imagination on your part.
That is a player who does not respect the narrative of his own fallen character and does not respect the stories of the other characters of the player, and does not respect the narrative of the game. If you really want to play the same character every time you lose one, then there are games that are based on exactly that.
Maybe I look at what atmosphere is creating or allowing it to allow this kind of thing to emerge and work to mitigate that. One way to evaluate the "health" of your game is to observe what is happening in the game and what is happening outside the game.
In character, do your game sessions flow organically from one scene to the next, with a variety of wonders, monsters and NPCs to find, or are they basically flashes from one piece to another, with monsters to kill and loot each time? Are there dramas between characters or the PCs are just statistical puppets for the players to greet the monsters until the monsters fall? Do PCs have strong personal relationships with each other, for better or for worse, or do all characters talk about the next tactical or logistical move?
If what you see is not what you want to see, then follow some steps in the character to solve it. Add variety to your scenes, increase the arcs of the story and reduce random monsters. Infuse the purpose in the actions of the NPCs, both monsters and people (the goblins have become desperate as trade has slowed down lately, reducing the frequency of looting targets, or the flower seller is so persistent because money helps her pay for her sick husband's care)
Outside the character, does the game speak of powers and mechanics instead of plotting twists and astonishing actions? Is it about the discussion about how much fun people had or complain about the rules and resolutions? Do players talk about each other's characters as people or as blocks of statistics?
This is a subtle way of encouraging players to embrace variety. If there is a richer world, players will tend to gravitate towards ways of exploring that world through the eyes of different characters.
Playstyle is important, including yours.
There's nothing & # 39; bad & # 39; about taking a mechanic player approach, however, based on what you have said in your question, it seems that you want players to expand their horizons a little and honor the story of their fallen character, not just say & # 39; oops & # 39; ; My fighter is dead. The next fighter! If Fred the Magician dies, and his identical twin brother, Ferd, intervenes to take his place, and is like Fred in all other respects, that hurts the game for everyone, including the Fred / Ferd player. As a GM, it's your job to make sure that does not happen. Often, all you need is a no, try again. to save months of irritation and headache, which will be displayed on the table.