Yeah I know--the Queen seemed to know everything (Shakespeare in disguise at Greenwich, the de-flowering of Viola De Lesseps, etc.)
But how in the world could she possibly know the made-up name "Master Kent"? She calls "him" by name at the end of the performance of Romeo and Juliet.
Possibly from the Master of the Revels? He was an official of the court. If she had heard of the scandal that closed the Rose, the business of a woman disguised as a boy player, she might well have guessed who this was.
The Queen would never have attended a public playhouse, of course; but for the purposes of the fantasy/comedy, let's agree that she heard of all this and wanted to see the play, incognito. She wouldn't have know that 'Master Kent' would be performing, of course, since Viola didn't know that herself.
But John Webster did not know Master Kent's name either (as far as we know).
"NOT HIM----HER!!!!!!"
They use that device a few times--not referring to a character's name to set up situations (like "Who is dead, my Lord" Oh--I did not think I would be the one to tell you. Only met the chap once at your house--a loss to writing and dancing" (referring to Marlowe (Wessex)or Shakespeare (Viola).
There is no indication that John Webster's knew Master Kent's name--or that he said a name when he "ratted" (pun intended) them out!
I expect everyone in London knew all about it, gossip being what it is. The boatman recognised Lady Viola de Lessops ("Known 'er since she was this 'igh. Wouldn't fool a child"), and he heard Will address her as 'Thomas'. Juicy bit of scandal to tell his next fare.
Which was produced backstage after the play had started, since nobody knew Thomas Kent was going to play Juliet until 'he' was conscripted literally at the last minute. Quick work with the Elizabethan photocopier, there.