I’m just assuming this, but I think the name of our Ciel is Sirius. The diviner did say,...

I thought Ciel was a Sirius star sign according to the blood scheme

That might be it.

If that really was Fake Ciel's real name, he wouldn't have just let anyone call him like that so casually.

There are many theory in Fake Ciel's real name. Like the one whre since Ciel means sky in French, then the other name would be Terre which means land in French.

I personally prefer the name Mer which means sea in French. Since both Ciel's favor the color blue, it will only be fitting that their name is sky and sea cause both the sky and the sea is blue.