The simple amswer is no,

one who is a sikh follows the teachings of the guru full stop. They do not have the rite to call them selves a SIKH let alone a SINGH.

If the great sikh mrtyrs were given the option to either have their hair cut or die why did they choose death?

because the kes (uncut hair) is the very symbol of our faith

in the ardass we say

"sikhi kesa swasa nal nibahi"

May all sikhs maintain their uncut hair aslong as they breath"

Sikhi isn't punjabi culture

sikhi isn't a namesake