In my opinion, if you do want to change your name then you should go all in to change it to exactly what you want as soon as possible and if at all possible get it changed on your foreign passport BEFORE your interview. Then you automatically start your whole new life in America with all your new US documents automatically coming with your desired name from day one with no further effort. If you find yourself with multiple names on your green card, social security card, state id, banking, employment and everything else, it's a huge hassle that can follow you around a very long time. I have no idea how hard it is to change a middle name on a Canadian passport but it costs at least $415 and can take over a year to change a name in a US green card once it's been issued in a non-desired name. Plus every other document and ID issued while waiting for the green card change. I could guess a Canadian name change might be faster, easier and cheaper. I would at least look into it and putting effort into going that way if at all possible. It is not easy after you get to the US.