Have three questionmarks for the scholar.

1)How is it known that the hedjet is the crown of Upper Egypt and the Deshret is the crown for Lower Egypt?

2)Is this a stated fact or theoretical?

3)At what time and how did egyptologists come to conclusion that it is/was like this?

Hi again Paw
I am not aware of any answers that directly answer your questions.
Perhaps one way the names of the various crowns is known is by their shines. The Deshret had a shine dedicated to it in Lower Egypt. Most likely in the temple of Wadjet in Butto. This took place about, 1904, when Amelineau discovered a year lable mentioning the shine. While the Hedjet had one shine at the Residence in Memphis, and possibility in the temple of Horus of Nekhen, at Hierakonpolis.

Then they might have known the names from the many inscriptions of Pharaohs wearing different crowns.
Then they may have been known by Greek names from the Ptolomic period.

The currently used names are accepted as fact.

Egyptianologists have been able to read the names of the crowns ever since Champollion in 1826, deciphered the ancient written language.

I am sorry i can't give you better answers to your questions. Maybe someone else can?