[ANSTHRLD] Looking for Help with a Roman Name

[Lee & Susan]

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Greetings!
Is there anyone out there who could help me with creating a Roman name?  I am looking for a name for a persona from the early Empire period, 1st - early 2nd centuries C.E.  From what I've been able to find, I would be using a name with two elements, nomen and cognomen, both in a feminized form.  My questions from there are primarily these:
1)  Which name would a person be called by their friends, the nomen or cognomen?
2)  I'm interested in using the name Drusilla, I've found Drusus listed as a nomen and (from my minimal understanding of Latin) the normal feminine form would be Drusa.  Would Drusilla be possible, also, as a feminized (possibly a diminutive form) nomen for a woman?

My sincere thanks to anyone who can help me with this,
Susan
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