Some states will recognize your foreign marriage certificate as lawful change of name document. Some, reported to include Colorado, will not, but offer a work around in the form of a re-marriage license, service, and certificate.
Changing name by naturalization can be difficult. The core problem is that in the U.S. only a judge can administer oaths of citizenship that include a change name. There are on the order of 1000 federal judges, and one million people naturalizing each year. Depending on the field office that can mean a longer wait. Some field offices will all but flat out refuse a change of name.
Even if you get a change of name oath, the actual change of name document is not the naturalization document as you might expect. When it does not show up, there can be a finger pointing exercise between the court and USCIS.
We sent it via SPEEDEX in Quetta, and confirmation said it was received but embassy continues to say they need original Nikkah Namah. (is that the two copies that you get once you submit it to the local office) Because we have that and also NADRA.