It was customary in those days, when a war hero such as David killed a well known enemy,
that the hero would travel with the enemy's head... and when entering a new city
would be welcomed at such a sight to see. That head became the keys to the city, and was
held, in high honor of the one bearing the head.
David kept the head with him for quite sometime. And, he kept the armor of Goliath as well.
It does not say David buried the head in Jerusalem, though he might have eventually done so.
That theory about Golgatha sounds more like tradition and folk lore.
As Saul watched David going out to meet the Philistine, he said to Abner,
commander of the army, “Abner, whose son is that young man?”
Abner replied, “As surely as you live, Your Majesty, I don’t know.”
The king said, “Find out whose son this young man is.”
As soon as David returned from killing the Philistine, Abner took him
and brought him before Saul, with David still holding the Philistine’s head." 1 Samuel 17:55-57
David kept the head with him wherever he went! Even before the King!
And, also to be considered....
Golgotha, (from Latin calva: “bald head” or “skull”), skull-shaped hill in ancient Jerusalem,
the site of Jesus’ Crucifixion. It is referred to in all four Gospels (Matthew 27:33, Mark 15:22,
Luke 23:33, and John 19:17). The hill of execution was outside the city walls of Jerusalem,
apparently near a road and not far from the sepulchre where Jesus was buried.
https://www.britannica.com/place/Golgotha
The meaning, "bald head," more likely referred to the appearance of a rock formation.
grace and peace ....................