Cingular is the name of a large US cell phone company, yet I associate the word cingular with pregnancy for some reason. Can anyone suggest what the connection might be?

I think they meant to be spelling singular in a cutesy, attention-grabbing way and ended up with a real word that means something not quite what they had in mind. It was the Word one Day back in Feb 03:

http://wordsmith.org/awad/archives/0203

Pehaps it's the cencation?

They probably spelled it that way to make it easier to trademark. (It's better than the name they had before which was Pacific Telesis, but the company in its ineptitude will always be Pac Bell to me.) Though the idea of a phone company girdling the world would perhaps not be unpleasant to the board of directors of SBC (new new name, except for the wireless service, which just bought AT&T wireless recently).

"Cingular is the name of a large US cell phone company, yet I associate the word cingular with pregnancy for some reason. Can anyone suggest what the connection might be?"

Here's my suggestion, inspired by the link to the AWAD archives:

"enceinte: adj. Carrying an unborn child; pregnant." (American Heritage Dictionary, 4th ed.)

I've always known the meaning of this word, but have often wondered what pregnancy should have to do with being encircled or wearing a belt. AHD4 says is goes back to Latin "inciens" meaning pregnant. Which fact still leaves me wondering. Now I will use up even more work time chasing the IE root.

SBC (new new name, except for the wireless service, which just bought AT&T wireless recently).

SBC is already taken. It stands for Seattle's Best Coffee and here's the story of how it got its name: http://www.seattlesbest.com/site/about/

I associate the word cingular with pregnancy for some reason

Maybe you're tied up in cellular ligation.