My wife is on student dependent visa but in both of each passport there is a no mension of spouse name, we have marriage certificate, my wife has national insurance number and in that as per passport i.e. after my wife name her father name is there, now I want to open my wife bank account so in which name I open her account by using her father name or my name after her name. Please give sugession

Your wife should know what to tell you.

Shouldn't you be discussing this with her? She should know what she wants or better yet what is best for her.