You can manually change the Adventurer's name by altering the save file. First you need to convert the .rpgsave file you wanna edit to a .txt, to do so you can use this website https://www.save-editor.com/tools/rpg_tkool_mv.html But I highly recommend you use an adblocker before you click that link.
Once the file is a regular text-file, you can open it and use the search function (Ctrl+F for most text programs) and look for the line
"_name":"Adventurer".
and change the Adventurer to whatever name you prefer. (I'm assuming you're using one of the prepackaged save files where the MC is simply called "Adventurer", otherwise you gotta look for the name the bunny has in the current save file.)
Then use the link again, but this time convert the .txt file into an .rpgsave file, and replace the old one in the game's save folder with the new one.