Eri (絵理) combines the Japanese e (picture, blessing) and ri (reason, jasmine) — meaning "blessed with reason" or "painted jasmine." Multiple kanji combinations.
Eri Kitamura (born 1987) is the Japanese voice actress; Eri Yoshida (born 1992) was the first female professional baseball player in modern Japan.
Eri 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 Eri reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.