As learning starts in the womb and the teacher- the nurturer is the mum, then the fetus is a Sikh- a student. The name Kaur or Singh as a Sikh is just an identity of the household one is born into for the legal purposes as in the birth certificates. In the US one has to give the name of the child to the hospital within a few hours so they can issue the paperwork.
On the other hand one becomes a Sikh through practicing Gurmat ideals but born a Sikh through traditions. One may choose to change his/her name later on if one changes to a different way of life or a religion.
Singh & Kaur are gateways to Sikhi. One has the freedom to walk out of them anytime. If Singh and Kaur were prerequisite to be Sikhs then Harmander Sahib would not have 4 doors to invite all mankind irrespective of anyone's hue,creed or faith nor would we have peoples' hymns from other religions in SGGS.
Tejwant Singh