The ticket needs to be purchased in the (old) name listed inside the passport. You may also have to provide a passport number, which obviously also needs to match the passport you wish to travel on.
I assume the change-of-name is due to marriage. In this case US law allows you to continue to use your maiden name for legal matters. We have previously (accidentally) purchased tickets for my wife under her maiden name, while her passport was already updated and it wasn't a problem, but this might vary from airline to airline.
As advised before, I strongly recommend applying for a new passport, which should be possible through your embassy. If you plan to travel soon, they often allow expedited processing (for a fee). You can often even get a temporary passport issued directly at the embassy (imagine you lost your passport and need to travel home tomorrow - such documents are generally accepted internationally.
You will (under normal circumstanced) be allowed to keep your current passport (invalidated by your embassy), due to the US VISA inside. For a while I had to travel with two passports constantly as you are not allowed to remove the US VISA.