Really faint hissing sound from my new 12v AC to DC Power Supply
There is no way to tell for sure from your description, but most likely this is just fine.  Some noise from switching power supplies is normal.

That supply almost certainly contains a transformer that is being driven at the switching frequency.  You can't hear that directly, but variations of that frequency can be in the audible range.  This is especially true if the power supply implements "spread spectrum", which is sometimes done to limit the maximum power of RF emissions at any one frequency.  Instead of a peak at one frequency, it emits at lower amplitude over a broader range of frequencies.

Again, most likely there is nothing wrong.