If the application was submitted from the UK then an Appeal date would be forthcoming in around 3 months. If however, the application was submitted out of country then an appeal date will not be allocated until at least 6 months.
If the appeal was from in country then I would appeal the decision as judges are more likely to use common sense having all the evidence in front of them, as the UKBA is known to be notoriously vague with their decision. If however, the appeal is out of country and time is of the essence then I would submit a new application.
I do not think the application was refused simply due to your surname, it most likely they did not review the documents provided adequately and hence made an incorrect decisions.
The extent you would need to address the issues in your previous application would be to refute all the reasons for refusal in your covering letter as well as stating that you have submitted evidence to aid your case. I
It will be a case of spelling it out to them word for word, unfortunatley the UKBA do make some odd decisions and it seems you have been unfortunate with your application.
If you are happy with answer, kindly click ACCEPT.