Dovile is from the Lithuanian Dovilė — possibly from Lithuanian dovis (gift) or dūsavimas (sighing). Dovile is one of the Lithuanian feminine names.
Dovile 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 Dovile reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.