Just a few minor refinements to Mike Z's and John's largely correct clarifications of how Cingular came to be and then became just plain AT&T:
In the beginning Bell created AT&T (with the assistance of a gentleman called Vail). AT&T was not just a phone company, it was _the_ phone company. It called itself the Bell System, because it integrated local and long-distance service with telephone equipment (or CPE), thereby inventing both "one-stop shopping" and the "triple play."
AT&T was a monopoly, but a legal monopoly. It was regulated by puppets in every state but earned a nice, comfortable profit. One could easily identify an AT&T subsidiary, because they all had a region or state in their name, along with "Bell," "Telephone & Telegraph," or something like that in their corporate names.
Many years after dividing night from day and land from earth, God decided to divide CPE and long-distance from local telephone service. He took the form of Judge Harold Greene, who, effective 1/1/84, smote the old AT&T. He divided the dead-end local service from the vibrant and competitive long-distance and CPE part of AT&T. Henceforth, AT&T would be LD and CPE only (CPE was later spun off to Lucent, which spun itself off to Alcatel). The 22 or so operating companies conducting AT&T's local operations were reorganized into seven "Baby Bells" or "Bell Operating Companies. The seven Baby Bells set up separate subsidiaries and through them acquired the cellular licenses AT&T obtained in the early '80s and continued acquiring more. Among these Baby Bell separate subsidiaries were BellSouth Mobility Inc (no common and no period) and Southwestern Bell Mobile Servies, Inc.
The next fifteen years were years of flux. In the 1980s and 1990s, Craig McCaw, whose daddy owned a lot of cable systems, acquired a great number of cellular licenses. He decided to sell, and AT&T was the high bidder. The former McCaw Cellular licenses thus became owned by AT&T Wireless Services, Inc. (ATTWS), a wholly owned subsidiary of AT&T. As other have pointed out, the executives of AT&T, faced with ownership of a competitive, profit-generating subsidiary, threw up their hands and spun it off in order to buy stodgy, reliable, money-losing cable television monopolies. Meanwhile, the FCC auctioned off a bunch of new "PCS" spectrum, and some of it it was bought up by the Baby Bells and ATTWS. Also during this period, the number of Baby Bell was reduced to four through mergers -- SBC, BellSouth, Verizon, and Qwest.
Cingular was created as a joint venture of SBC and Bellsouth that, in2000, acquired the mobile properties of SBC (Southwestern Bell Mobile Systems, Inc., and other companies; the SBC mobile properties included many acquired through mergers with Ameritech, PacTel, and others) and BellSouth. Cingular was owned 60/40 by SBC and BellSouth, but control was shared 50/50.
Then Cingular acquired ATTWS, which at that point used the AT&T name but was no longer owned by AT&T. A change in name for the ATTWS properties was necessary because ATTWS's licensing agreement with AT&T for use of the name was only for a limited time. Cingular sought to integrate these systems with its own into a single network.
Then SBC acquired the shell of its long-separated parent AT&T and decided to use the parent's name, AT&T, for the resulting company. As a result, Cingular became owned by AT&T and BellSouth at about the same time as the AT&T name was phased out for the former ATTWS properties.
At the end of 2006, AT&T (i.e., SBC, after the renaming) and BellSouth merged. One of the key pieces of the merger was Cingular, which would now be wholly owned by the new AT&T. Cingular's profitable wireless operations were one of the factors driving the merger. The resulting company is AT&T, Inc. Its logo is "at&t", but the corporate name and the prhase used in the company's official correspondence is AT&T (uppercase).
Michael D. Sullivan Bethesda, MD (USA) (To reply, change example.invalid to com in the address.)