US, New Jersey—Geographic Birth Index, 1901–1929 [M3PG-YQT]
There are clear instructions and examples for name entry when parents' initials are provided instead of the child's given name (the surname field is used for the father's, mother's, and child's surname). The instructions don't say what to do for surnames when the child's given name is provided.
The examples don't cover it either - the example with the child's given name doesn't show entry fields for the father's and mother's surnames.
This batch has entry fields for all 3 surnames, but the document lists only one surname.
I lean towards leaving the surname fields blank for the father and mother, if the child's given name appears, but can take instruction.