Can I reserve a Bulgarian company name while documents are notarised abroad?

Yes. A name reserved with the Registry Agency on form D1 is held for 6 months, and only you can register a company under it in that time. The reservation can be renewed for another 6 months and does not oblige you to register. It is a sensible step when notarising and apostilling signatures abroad takes a few weeks.

Source: Choice and reservation of company name, Ministry of Economy, Investments and Industry, Republic of Bulgaria