Yes, there is an M in "name" (3)
I believe the answer is:
amy
'name' is the definition.
'yes there is an m in' is the wordplay.
'yes' becomes 'ay'.
'there is an m' becomes 'm'.
'in' indicates putting letters inside.
'ay' enclosing 'm' is 'AMY'.
(Other definitions for amy that I've seen before include "- Johnson, Eng. aviatrix" , "Girl's name; 3 dn (anag.)" , "--, Johnson, solo flyer" , "Record-making British aviator, Johnson" , "Youngest of Little Women" .)