“It's A-547, under Frank.”
For reservations, under introduces the booking name: The reservation is under Frank. The reference number is A-547 and the booking is in Frank's name.
A2-32 / CEFR A2 / EPISODE 32
Changing a restaurant reservation
SceneFrank phones a restaurant to change a booking.

WORDS & CONTEXT
For reservations, under introduces the booking name: The reservation is under Frank. The reference number is A-547 and the booking is in Frank's name.
Move something to … changes a booking or event to a different time. Frank asks to reschedule it for next Saturday.
As a verb, seat means to lead a customer to a seat or have them sit somewhere. Please don't seat her near … requests a particular seating arrangement, a common restaurant use.
Here go back means to return for more food. See A2-05: Tina went back four times on the previous visit.
Far from ... means at a distance from something, and here then means "in that case." Accepting Frank's explanation, the host agrees: "A table far from the dessert station, then." The punchline is that the host responds seriously to Frank's exaggerated worry that Tina might eat the other guests' share. The table is not just at the back of the restaurant; it is specifically away from the desserts.
Two more friends means two additional friends, and four of us means the four of us in total. Frank adds two friends to the original reservation for two, making it four. The next line, My friend Tina is coming., simply mentions that Tina will be there; it does not say she is one of the two new guests.