I have looked at only a few NJ "Certificate and Record of Death" for the period 1904-1910

Although they all include a space for Father's Name and Mother's Name on the pre-printed form, what is actually recorded varies. Up until 1909, the form asks "Mother's Name" and some of the ones I have seen list married name, others have maiden name.

It would appear that about 1910 the pre-printed form began reading "Maiden Name of Mother"