Begoña is the Basque name from Begoñako Andra Mari — "Our Lady of Begoña" — the patron saint of Biscay, Spain. The 16th-c. basilica in Bilbao houses the Marian image.
Used widely in the Basque Country.
Begoña 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.
In Pythagorean numerology the letters of Begoña reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.