Efrain

There may or may not be a fee to change the name on a particular document (i.e. a new driver's license usually has a fee, a new passport has a fee, a new Social Security card does not have a fee, etc.).
There is no additional fee to actually change your name...the marriage certificate already permits it. You just have to use the new name, and update documents as you can.

Hey ! I am moving in October to DC, K-1 as well! And from what we know, we just go straight to court house and get Marriage Licence there!

Did you and your fiance discuss this prior to your arrival? 

Yes. AP is a normal part of the process. Usually it is days. Sometimes weeks. Rarely months or longer. AP covers anything after the interview, including final checks and printing of the visa.

Welcome to the forum.
 
While you are waiting for a response to your inquiry. I was trying to get more info about you from your timeline. However, it is empty,  It helps everyone that uses the forum. Additionally, it helps make the VJ stats more relevant.
 
Good luck on your immigration journey.

~~Moved to the Regional forum, from K1 Progress Reports - THe OP is looking for country specific answers~~

Yes. Finish the treatment. Then go and complete your medical exam.

Just started my first treatment today and I need 2 week more so after I finish I should do the medical exams for my visa?thank tou

If you are positive for Syphilis 
Are you asking if a recent positive test for syphilis is a problem, then the answer is yes.  You might require treatment before the exam form can be completed.

My husband lived in England for his college years and he needed to provide a certified police certificate from Spain and England. I'm not sure where he received it but I believe he went to the Court and they were able to advise him to where he was able to go. Also, above is correct. You will receive packet 3 in order to send in the necessary documentations, then will need to wait for packet 4 in order for you to book your medical/interview.

My husband is from Malaga and had his interview in September