wife visa - maiden name

I am a citizen in a non EU country.
I have been accepted as PhD student at a university in Scotland. The courses will begin in three months and I want to take my girlfriend with me in the UK. We want to get married and she will apply for a wife visa.
I have some questions about the process of obtaining the visas:

1. Does she have to take my name after the marriage? Will the people from the embassy be suspicious if she keeps hers? We live together for almost 4 years but we cannot produce any physical proof of this cohabitation.

2. My scholarship will be about 900 pounds per month(for living expenses). What amount of money should we have (minimum) in a deposit in order to be considered that we will not apply for public funds.


3. I haven’t taken my visa yet. Should we go together to the embassy and request the visas at the same time?

4. Because I will leave for UK in September and my girlfriend probably in November, there will be no accommodation arranged for us at the time of the request for the visas. Is this a big problem?

Thank you in advance for your answers.