You certainly don’t have to, although many parents do. In the beginning, one pair would be wise, just in case, your child decides not to continue wrestling past the first season. Once they’re sure about going back for season two, we recommend two pairs--one for practice and one for competition. Whether they should be the exact same pair is largely up to your child, though many children do get used to a certain fit and feel.
Overall, we recommend sticking with shoes that at least have a similar build and design, so that your child isn’t thrown off between practices and competitions. You can also choose to buy a fitted pair, and a half or full size up to have as a spare. Foot growth seems to happen practically overnight for some children, so thinking ahead may save you the aggravation of trying to secure shoes right before a tournament.