Gabija

As far as I know, it does not derive from "gaubti", the name is usually taken from the pagan goddess Gabija. While she's mentioned as a goddess of fire, it should be specified that Gabija was the goddess of hearth and home, warmth and light of the home, and such. In pagan homes fire was given a special care and respect: fire Gabija would be waken up in the morning by lighting it, then kept through the day, and in the evening it would be 'taken to bed' by covering it with ashes in a special rite. Therefore Gabija is considered to be a name for a hospitable and warm person, and a girl, when given this name, is probably expected to grow up to hold these characteristics.

Gabija - Used to be a Lithuanian Goddess. The Goddess of Fire. Also known as a Guardian of "home fire place". People used to believe that "Gabija" is protecting home.

The name Gabija is derived from 'gaubti' meaning 'to cover'. [noted -ed]

It means 'to solace' in Lithuanian.