Yes, I know what you mean: when I register myself here I and my kids, I get the name of my father and grandfather too and my kids the name of their father and grandfathter, it is so different then in our passports.
Your ambassy is right but you have to keep in mind that the Jordanian law is different: she will get after her first (or second) name the name of her father and grandfather from your husband side. You can't change that.
For the US she get the names according to the US law.
That's why you have to travel always with two passports: when you want to leave and enter Jordan, you have to use the Jordanian passport, and when you enter or leave your country or an other one, use your US passport.
There are some cases where it is better to use the Jordanian one.