I don't like the name. I know that sounds maybe trivial (and it might actually be!). But it sounds like some kind of national care program. As most of us know, the US only has ObamaCare (aka the Affordable Care Act) which is actually health insurance reform. (As well as some programs for certain groups like the VA, Medicare, Medicaid, sChip and so on.) Lots of good things in ObamaCare, but not really a national care for EVERYBODY.
The use of the name in a private company to me could describe a company that might be trying to swindle people or get people to think this is not a private company like Aetna or United Health Care. BTW, I had something with a name like that before. It actually was funded by MEGA which is, I think, the singlehandedly worst insurance company in the US.
I may be totally off here. And sorry for my mini-rant on the US "health care system".
--Jay Jay