ζ = Z (z sound)
ω = o (long o sound)
ή = i (ee sound)
Therefore, ζωή = Zoe. Zoe is the English transliteration from Greek. Zöe is the Dutch transliteration from Greek, meaning it's the Dutch spelling of the Greek word for life.
In answer to your question, yes, ζωή means life. It is the root of words like "zoology," which is the study of life.
Oh, by the way, the name Greek word "ζωή" originally derives from the Hebrew word "חוה," which is "chaweh," means "to live," and is also the Hebrew name Eve. The Hebrews pronounce Eve not like we pronounce Eve in English but much more like the name Zoe with the Z sounding more like a Ch. So Zoe originally traces back through the Netherlands, through Ancient Greece, and back into Hebrew to the name Eve.