In order to apply for citizenship with the correct name, the name you use must be your legal name, meaning you cannot just use a name you prefer or want to be called. If you are married, there is no need to get a court order to change your name - the marriage certificate is sufficient to change your legal name. However, marriage does not connote a change in your middle name. I have seen immigration officers okay with name changes like this and others who demand a court order showing a name change occurred. A social security card and drivers license are not legal documents. To be safe, the best thing is to obtain a court order from the county court in your local jurisdiction indicating that you have changed your name. You can likely obtain this information online or call the county clerk's office for more information.