Andrea,
Save yourself from worrying about this and just create a new clone in a different directory and once you are happy that it is working the way you are used to, just delete the original one since you are no longer using "mio" and rename it if you want to use the original name.
cd [new_directory_name]
git remote -v (will show you that the fetch is what you just used)
git pull (will reply with "Already up to date.")
And you never have to worry about "git push" because it will not let you for this particular repository.
Alternatively, if you want to do it using your current directory and are not concerned about something you did in the past messing it up (I had this problem because of the weird things I do):
git remote -v
git remote remove origin
git pull origin
I learned more about git then I ever wanted to know in the last few weeks and it does not care what you name things.