Yes to both sides.
Plebe should be equipped with desired sponsor's name, because at some point during the summer, they will fill out the sponsor request form, if they want one. The requested sponsor must be in the sponsor coordinator database and current on their training. Bonus would be to get the actual sponsor's assigned number. It's on all the sponsor correspondence or easily obtained from the sponsor coordinator. That way, it's absolutely clear which family the plebe is requesting.
Sponsors already listed in the sponsor coordinator's database receive a letter each summer asking if they wish to take any plebes that year, how many, etc. That's when we put in any special requests. We have had 3 sisters from the same family, 2 brothers, and other special requests from out-of-town friends whose son or daughter is heading to USNA. Amazing how many of our former Navy shipmates with whom we served as LTs with babes in arms, now have USNA-age "kids."
If things are done similar to previous years, there will be a Sponsor Social the Sunday afternoon of the weekend prior to Plebe Parents Weekend. That's a meet-and-greet where sponsor families come to Alumni Hall, get their list of assigned plebes, find them and have a chance to chat. Last-minute tweaks are often done there. We might lose a plebe who was supposed to go to someone else, and gain two whose sponsors backed out.If, by chance, your plebe loses or forgets the desired sponsor's name, as long as he or she can connect with the desired sponsor and get to the sponsor coordinator's tables, it can be sorted out. Key thing is the PLEBE's request is the determining factor for the official reassignment.
Best way is for the mutual request to be done at both ends.
Oh - for the authoritative answers, consult the USNA sponsor page at
http://www.usna.edu/Sponsor/