Solveig comes from the Old Norse Salveig — composed of salr (house, hall) and veig (strength). The name is sometimes interpreted as "strong-house" or "strong woman."
Solveig is the heroine of Henrik Ibsen's verse drama Peer Gynt (1867) — the faithful woman who waits for the wandering Peer for decades. Edvard Grieg's Solveig's Song from the incidental music is one of the most famous melodies in Norwegian music.
Solveig is a compound name. Its parts are sól + veig — each an attested element with a recorded meaning of its own.
Solveig 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 Solveig reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.