Comparative law notes
This probably is the most accurate translation, but the word "orderer" or "ordering person" will be greeted with curiosity among English-speakers since they are not at all common words or phrases. Even though a person ordering a good or service may not yet technically qualify as a customer or purchaser (since its order or offer is not yet accepted) and hence its status as merely a "Besteller" is legally justified, English-speaking lawyers and business persons will nevertheless feel comfortable calling the ordering person a "customer" or "buyer", even if that person has not yet graduated to that status in the contracting process. German lawyers may find this sloppy, but it is nevertheless established practice in the Anglo-American business law world.