Registration is obligatory in Bulgaria and required by all operators. The whole process is pretty simple as the salesperson will do everything for you.

Thank you.

By the way MTel offers a "Prima Data" SIM card without the need to register ("bez registraciya" / "без регистрация") which is limited to data only (no voice) but actually data packs are cheaper than for registered SIM cards:
2GB valid for 14 days for 9.90 BGN (€ 5.06) and
5GB valid for 30 days for 24.90 BGN (€ 12.73)

for details see: http://www.mtel.bg/prima-predplaten-mobilen-internet (it seems like Mtel has discontinued the English version of its website)

As some salesmen are not aware of this SIM card you have to be very careful because if they register your ID your desired "Prima Data" SIM card it automatically becomes a regular "Prima" SIM card with more expensive data tariffs. So do not show your ID in case you want this "Prima Data" SIM.