Rename Minecraft Advancements without removing them

A resource pack can rename everything by changing the lang file for translations. If your resource pack (a normal zip file, or filesystem folder, that you put in the resource pack folder you find at Settings > Resource Packs > Open Resource Pack Folder) has a assets/minecraft/lang/en_gb.json file in it, you can change the English (Great Britain) language to say, for example:

{
    "advancements.nether.find_fortress.title": "Siege",
    "advancements.nether.find_fortress.description": "Break down the walls of the blazes' castle"
}

If you open your .minecraft folder (one above the Resource Pack folder), you can find a assets/indexes folder with .json files in it; each of these will describe mappings of names (names you can overwrite in your resource pack's own assets folder, like minecraft/lang/en_gb.json) to a SHA-1 sum of the contents of their entry in the default resource pack. You can then find the original file in assets/objects under the given SHA-1 sum—this will allow you to see what the language file originally had in it, so you know what to overwrite. Unlike other resource pack files, language files are combinative and not directly overwritten—you do not have to write the entries for things you don't intend to change.