not necessarily.
BZP has two nitrogen atoms (since it's a piperazine). it would be possible to protonate both of them, and the pH at which both would be protonated would be lower, of course, than the pKa at which one would.
therefore, it would be possible to prepare BZP as both the hydrochloride and the dihydrochloride, and there will be a difference between them.
BZP dihydrochloride contains only 85.3% of the BZP of BZP hydrochloride, because of the extra HCl. also, BZP dihydrochloride, being more acidic, may have different absorption characteristics once it's in the body.