Nice lady using first name to interrupt me (6)
I believe the answer is:
madame
'nice lady' is the definition.
(title for a woman in France eg in Nice)
'first name to interrupt me' is the wordplay.
'first name' becomes 'adam' (name of the first human**).
'to interrupt' means one lot of letters goes inside another.
'adam' inserted into 'me' is 'MADAME'.
'using' is the link.
(Other definitions for madame that I've seen before include "A French-speaking woman" , "Book by Flaubert" , "French Mrs" , "Married woman abroad" , "Frenchwoman's title" .)