If a certain user is banned, their UUID is banned. That means that if they change their name, they still can't go on. The only way to bypass a ban is to use a different account. Using proxies wouldn't allow you to get back on to the server if the UUID/player is banned.
universally unique identifier - every minecraft account has one
it's a way of identifying users if they change their name
if I change my name, my UUID is the same
my UUID is cf1f3b31-3b7b-44a9-82a5-82b2984f183a
Comments on Profile Post by MatthewStevenGo