a testing company, like Underwriter's Labs is for physical goods
A single testing company, like UL? Now, don't get me wrong - I've every bit as much confidence in UL's certifications as I have in TUV's. Or Det Norske Veritas'. Or BASEEFA's. But in the real world, one certifying company is just not going to cut it. And it doesn't, as the above list of the certifying authorities (with whom I have had to deal with often enough to remember their names) suggests.
There's an XKCD for that. xkcd.com/927/
Actually, the situation isn't quite as bleak - for hardware - as 927 suggests. There are widely applicable standards organisations for many things (I can add IDEST to the above list!) which are fairly well established in those fields, and which consequently have troubles with people counterfeiting their trademarks to falsely claim approvals that they don't have. But it's not a single unitary authority. And I doubt that one code-tester agency "to rule them all and in the lightness bind them" would happen for software either. Several bodies