Start to check everyone's name (4)
I believe the answer is:
call
'name' is the definition.
(a name is a call-sign)
'start to check everyone's' is the wordplay.
'start to' suggests taking the first letters.
'everyone' becomes 'all' (I've seen this before).
The first letter of 'check' is 'c'.
'c'+'all'='CALL'
(Other definitions for call that I've seen before include "Phone - demand" , "Telephone - give a name" , "Assign a name to" , "Hail; visit" , "Be in control" .)