'Abd, as far as I know, is exclusively masculine; as such, it wouldn't make any sense to use it as a girl's name.
The female equivalent would be Amat, which use has dated back to the days of the sahabah (according to the scholars at Islamweb). Grammatically, it connects to the Name of Allah the same as 'Abd would:
- 'Abdullah (عبد الله: male servant of Allah) => Amatullah (أمة الله: female servant of Allah)
- 'Abdurrahman (عبد الرحمن: male servant of ar-Rahman) => Amaturrahman (أمة الرحمن: female servant of ar-Rahman)
As for the practice of dropping the prefix Al-, even though God Himself is neither male nor female the Names used to describe Him are using the male gender. So, again, using these as a girl's name would be odd.
In Arabic, the feminine suffix -ah can be added to create a female name from a masculine adjective; this can, I believe, be done for any of the unprefixed Names of Allah that would otherwise make a valid name. Muhammad's own foster-mother, for example, was named Halimah, which is the feminine form of Halim (forbearing). As far as I know she was named before the advent of Islam, so this doesn't necessarily mean that the name was actually derived from the Name of God (Al-Halim: The Forbearing) directly, but the naming of people by such common adjectives was a regular practice both before and after the time of Muhammad.