Eliza is a short form of Elizabeth — from the Hebrew Elīšeḇaʿ, meaning "God is my oath." It came into widespread use as an independent name in the eighteenth century and has remained in continuous use ever since.
More recently, the musical Hamilton has brought Eliza Hamilton (Alexander Hamilton's wife) into contemporary consciousness. Today Eliza sits in the U.S. top 100.
Eliza 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 Eliza reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.