On board ship, and during formal dining, military are announced as:
"Commander, Alpha Two-Six.... Arriving"
And the "Arriving" is timed specifically for the moment they are formally "entering" the room; specifically as they cross the threshold.
The Germans do something similar, and say "heir ist... Baumann" (or whatever), also timing it for the cross of threshold.
So, saying "Alexandra, daughter of the Ducal house... has arrived/greets you/be happenin/(whatevs)" would really make sense in an informal (for royalty) meal setting.