We're Canadian. We live in Canada, not the US, sorry for not explaining that.

The equivalent Canadian website says: "Always use your Canadian passport if possible, especially when entering the country of your second citizenship."

Note the "if possible" - there is no blanket prohibition (and how could one be enforced?) However, this warning seems to relate mostly to the problems that might arise if you needed consular services in a country like Iran or Saudi Arabia, or the possibility of being required to perform military service in, say, Greece if you had Greek nationality.

WWanderer - you haven't answered the question in my post from Aug 31, 10 at 9:39am

"I watched my son try this, and he was told that he should choose one passport and use this one only" - precisely where did he "try this", what exactly was "this", and who told him to use one only?

Oh, sorry. This was at Pearson Airport, on the way out on a flight to the States.

Oh, well presenting two passports to immigration on the way out certainly is at best unnecessary. The only time I do it is at check-in on the way back to the US, to prove to the airline that I will be able to get in (and to match my PNR details).

Well now when we fly to the States and back we have to enter our passport numbers in advance or at check-in, so I don't think using two different ones would be an option.

Sigh. I show the US one, and enter it for the PNR, for getting back into the US. I show the UK one for getting out of the UK, or wherever. I show both to the airline in case they need to run the UK one through the system to match the entry records. I show the UK one to the UK immigration officials (on entry and exit) and the US one to the US immigration officials (on entry and exit). It's really quite simple.

comments are all well and good - some are informative too. But the OP's situation is not as simple as dual citizenship (and US/UK couldn't get any simpler). OP's question involves 2 passports with 2 different names, even if one is only a shortened version of the other.

greekcanadian - I agree with brotherleelove = talk to the closest greek consulate you have in canada, and go from there.