Branch is collected at the account creator level and "trickles down" to the readers in the group. If you are registering someone for a program who already had a branch assigned in the past, you will just need to update the branch affiliation at the account creator level to ensure the correct branch gets "credit" for the reader.
To do this, you go to People > Find a Person. Then, find the reader. In the example below, you may be searching for Avery, but would click on the "edit" button next to Tiffany Zootest because she is the account creator.
Select the updated branch and save!