Probably a variant of Ginny, a diminutive of Virginia or Jennifer.
Ginneh is probably a variant of Ginny, a diminutive of Virginia or Jennifer. As a result, it feels like a nickname-shaped name that has drifted into independent use.
The spelling gives Ginneh a slightly more modern, personalized look. It sounds friendly and informal, with the easy warmth of a diminutive, but the ending makes it feel more deliberate than casual. That combination often gives such names their charm.