My wife's surname, translated into Hungarian, is in her passport. Our surnames are not the same now; it is different and in our marriage certificate. Will we have problems with the application because of this? I am a non-EU citizen and we want to travel together to the UK. When you look at our passports, you see two different surnames. What should we do about it?
Having matching names is not a requirement for the EEA family permit. You need to provide documentary evidence of your relationship. For a married couple, this generally means your marriage certificate.
You also need to supply the passport of the applicant, of course, and the proof of EEA nationality of the EEA family member, which is usually the national ID card or passport. If your wife's name (or yours) does not match between the marriage certificate and the passport, you will need to show some evidence to show that the two documents refer to the same person.