Ene is from the Estonian ene (mother, nurturer) — also possibly from the broader Finno-Ugric enä (great, large). Ene Mihkelson Institute — Estonian cultural institution. Princess Ene — modern Estonian heritage naming.
Ene 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 Ene reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.