I suppose it depends on the ID that the tower transmits, and whether your
phone or your SIM card has precedence in interpreting that number and
converting it to a text string - and which of those lookup lists is more
up to date. Apparently there are some towers that Cingular acquired in the
AT&T merger, but are still transmitting the AT&T code. If you had a
Cingular SIM card and branded phone, all you would ever see would be
"Cingular".

FWIW most of my unbranded phones display "Cingular Wireless".

The phone does a table look up in the ROM of the phone to determine
what carrier name to display.

The ROM in the phone usually determines what is displayed as the
carrier. Your phone picked the carrier that is identified in the ROM
as AT&T, however if you were to buy a telephone today, that ID would
be in the ROM as Cingular. Some old GSM phones will ID GSM service in
New Zealand as Bell South, because Bell South was the operator at the
time the phone was built. The actual carrier for the past decade or so
has been Vodaphone, who bought Bell South GSM operation in New
Zealand.