As people, we have a given name and a family name, and often a second given name, as a homage to a relative.
Yet, they ask for a first name and a last name and a middle name or middle initial.
I think this means the first part of the name, the last part of the name, and the middle initial, which is the middle part of the name.
The name is JOHN T SMITH. It is the name of a persona/franchise such as BURGER KING.
For the name BURGER KING, the first part of the name is BURGER and the last part is KING.
Or more succinctly BURGER KING’s first name is BURGER and the last name is KING. BURGER KING does not have a middle initial or a middle name.
For the name/persona/franchise JOHN T SMITH. The first part of the name is JOHN. The last part of the name is SMITH and the middle part of the name is T.
That’s the only way it makes sense to say first/last/middle.
I do not have a name. I have a given name and a family name, but I do not have just a ‘name’. Ships have names.
It’s a subtle but critical difference.
When people ask for my name, I either say, “Well my given name is ______” or I might say, “I’m called _______.”