Abeba (አበባ) is the Amharic word for "flower." The Ethiopian capital is Addis Ababa ("new flower"), founded in 1886. A traditional Ethiopian feminine name.
Abeba is widely used in Ethiopia.
Abeba 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 Abeba reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.