Sites like tstd.org will test anonymously for STDs. You will have to pay for it out of pocket. Essential a doctor there orders the test, and lots of labs will allow you to use use a number to sign in. Some will require your name.
Of course, infidelity aside, you'll have a moral obligation to tell your wife if you do test positive, at least in my opinion.
Good luck.
I don't know that there are any places who will do anonymous testing for stds. Many will do anonymous HIV, but not stds.
However, if you go to a clinic, and get tested, they have to adhere to the same confidentiality laws that your regular doc does.
Some places won't push it if you refuse to give some info, others will.
Its really important that you get tested, and that if you have anything, that you tell your wife, as she could have it to, and you'd just end up re-infected. It could also cause her a great deal of pain in the long run if she has something that's untreated.
AJ