I agree with this, as a K1 visa holder you are eligible to get a SSN, but the window is very limited. This is what we did. Get the SSN although it will be in the maiden name it will not be any problem to change to the married name later if you wish. Be sure to get your I-94 before applying for the SSN. That can be gotten from the I-94 website online be sure to print out several copies as you will need them later. SSN is most important and its a very easy process the sooner you apply. Some states do require a SSN to apply for the marriage license so you'll have to check your state requirements. The key is start building for your AOS NOW and with a SSN it makes it all the better.