According to Katana, the Ishimura Clan chose this name for her because she must have possessed similar qualities to that of the sword of the same name. Other details of the Ceremony are unknown, but Katana notes that she willingly accepted the name (while also noting that she would not let the name define her), indicating that she was not obligated to adopt the name the clan determined. ("New Rules")
It remains uncertain if this ceremony continues to be practiced in the modern day, or even if gargoyles in other parts of the world have adopted similar rituals with their clans.
In 1997, Brooklyn explained to Katana and Broadway that when it comes to the egg nicknamed "Egwardo", they will determine a true name after they "get a feel" for the gargoyle that eventually hatches. ("Idyll Or Nightmare")