There are many people who introduce themselves in Asura Kingdom as Greyrat.
However, though an ordinary name, the talk becomes different when it’s about a genius.
For nobles who wish to be established, they need to have blood relations with one of the four main branches of Greyrat, no doubt he had been working towards that end.
That he started out with the Boreas, by being hired through Philip, Sauros's so-called illegitimate child, was also guessed at.
At least, something like a betrothal to Boreas' shrew-like daughter could make it so he could claim the name.
Luke says that none of his family, brothers or anyone has a boy with that name.
[It will be necessary to examine it more in detail.]
Nobles very much loved thinking of things to do with power struggles.
If Rudeus chose someone other than Notos, plans would be crafted to sabotage him.
However if he chose Notos, there is a chance he could be enlisted as an ally.
And so, their talks deviated from the original purpose of validating the identity of Sylphy.
To them, the possibility of a power struggle was of far more important than anything trivial, like the true nature of Sylphy after all.