Post

I agree with @oliphant that best option is probably creating a new account on the same server and then migrating your old account to the new account. This will let you keep your followers/follows/etc and keep you on the same server, but provide you with a new handle.

The posts are an issue. If you're comfortable leaving the old handle visible the old posts will redirect to your new account, but if you want to delete the old handle the old handle's posts would be deleted too.