My sister created my Mii in my stead. I tried changing it's appearance and name, and it looked like it worked by looking on my own 3DS, but on my friend's it's still the same. Is the problem on my end, and how can I fix it if it is?
If you are referring to your Mii's appearance on your friend's Streetpass Plaza, then you would need to Streetpass with your friend again for it to update.
If you are talking about the "Friends" application on the 3DS, your Mii should update on your friend's 3DS automatically with an internet connection.
It should do it automatically, if not then you would have to change your mii manually on the 3ds.