Thomasina is the feminine of Thomas — from the Aramaic tā'ōmā (twin), the apostle Thomas of the New Testament. A vintage revival name in the modern aesthetic. Thomasina, the Cat Who Thought She Was God (1957) — Paul Gallico's children's novel; adapted by Disney as The Three Lives of Thomasina (1963).
Thomasina 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 Thomasina reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.