After marriage, changing a name, obtaining residence permission
If you and your bride have opted for her to change her name on marriage then the next step is to get the change reflected in her passport. This is a fairly simple process and, as it depends just on the Russian consulate, it should be the same wherever you live.
Assuming that you opted for this, the marriage certificate will state that the name change was requested by the couple.
She must take her passport and the marriage certificate to the nearest Russian consulate. There, on payment of a fee (DeM50 when we went) the name will be changed in the passport with a nice official stamp.
You may need to have the marriage certificate translated into Russian. The first time that we went, the consular official turned us away because we did not have a translation. On the second occasion, we saw a different official and he did not ask to see a translation.
Unless you live close to the consulate, I think that it is better to have the translation with you before you go.
The next step is to apply for residence permission for your spouse and any children as appropriate. They will be entitled to the same residence permission as you. So. assuming that you already have an Aufenhaltserlaubnis, your spouse will be entitled to one with the same duration as yours. This is all described on my Aufenhaltserlaubnis page.