Birtukan is from the Amharic ብርቱካን (Birtukan — orange / orange-tree). Birtukan is one of the Amharic feminine names — central to traditional Ethiopian Orthodox heritage. Amharic feminine name reflecting Ethiopian Orthodox heritage.
Birtukan 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 Birtukan reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.