The following code does work correct when Name = "a" and otherName = "A":

dbContext.Table.FirstOrDefault(x => x.Name.Equals(otherName, StringComparison.CurrentCultureIgnoreCase));

I have found this when looking in the google:
http://stackoverflow.com/questions/5080727/string-equals-not-working-as-intended
I'm guessing that one should build the string columns with NOCASE by default and have an attribute to change this behavior?
Thought are welcomed.