Assuming that the HOA duly adopted the rule that requires this disclosure, probably yes.
An HOA is not subject to the privacy law or constitutional restrictions of a governmental entity, an HOA is the de facto owner of the common areas of the HOA, and in general, a private property owner can insist on getting any information the private property owner wishes as a condition of using a private property owner's property.
Generally speaking, however, the declarations of a condominium set forth the process by which rules like this one can be adopted and those rules have to be followed for the rule to be valid.