Oh just stop it, please. This is how a wild ASSumption becomes urban legend.
They did NOT change the name of ANYTHING to "lowercase" at&t. For some unknown reason (no doubt a marketing committee), they elected to have it APPEAR that way in the logo. That's it; logo only. The name of the company is AT&T Inc.
Check their Annual Report, Press Releases or any other company document you can get your hands on ... check the stock symbol (T). Just like, at the end, SBC no longer "stood for" Southwestern Bell Company; it was just SBC Inc. The new AT&T is just AT&T. It is not an abbreviation like the original was ......... and it is not LOWERCASE.