The name of your Patron Saint is given to you as a middle name when you enter the Church. It’s recorded on all of your official documents in the Church, and you become known as [Firstname] [Confirmationname] [Lastname], so for example, if your name is Jane Smith, and you take St. Teresa as your Patron Saint for Confirmation, then all of your Church documents would refer to you as Jane Teresa Smith.
When you are Confirmed, they also use your new name to Confirm you, so, in this case, the priest would say, “Teresa, be sealed with the Holy Spirit,” because the person’s Patron Saint is St. Teresa.
But if you don’t let anyone know before the time of Confirmation that you want to take the name of a Patron Saint for Confirmation, then this wouldn’t happen. (It has to be before they start making up the certificates, which happens usually a few weeks before Easter, so you really do want to get on this as soon as possible.)