Gaines is from the Old French gaignier (to gain, to acquire) — historically a French Norman surname. Gaines Award for Literary Excellence (since 2007).
Gaines 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 Gaines reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.