Can women address themselves as adiyen and dasan or are there any other suitable words? I have been intending to ask this for a long time and am using this platform to clarify my doubt. Thanks.

Adiyen is a common term used for addressing both genders.
While adiyen refers to self, adiyaal and adiyaan refers others.
Notes:
Dasi is the female equivalent of dasan, but in today’s context, that name does not bear good meaning hence it is not in practice.
Thirumangai Azhwar had said ‘adicci’.
The Sanskrit word Dasa is common to both genders and is used in Vedic rituals.