Name: monarch is call Alice to start with (5)
I believe the answer is:
erica
'name' is the definition.
'monarch is call alice to start with' is the wordplay.
'monarch' becomes 'er' (abbreviation for Elizabeth Regina).
'to start with' says to take the initial letters.
The first letters of 'is call alice' is 'ica'.
'er'+'ica'='ERICA'
(Other definitions for erica that I've seen before include "Girl's name - heather" , "growing up on the moors" , "Plant of the heath genus" , "Heath genus; girl's name" , "Woman" .)