Blagovesta is from the Bulgarian Blagovesta (Благовеста) — blago (good) + vest (news) — good news, Annunciation. Blagovesta is one of the Bulgarian Marian-devotion feminine names — referring to the Annunciation (Благовещение, Blagoveshtenie) feast day (March 25) when the Archangel Gabriel announced to the Virgin Mary that she would conceive Jesus (Luke 1:26-38). Central to Eastern Orthodox + Byzantine religious heritage.
Blagovesta does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Blagovesta reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.