Passing an entity to use it's fields to update method is ok to do?
The second one seams to me a better approach but you say that the ManID is a primary key, so why are you handling it as a non primary key and using the query result as a sequance?

public DbResult Update(int idToLookFor, string newName)
{
    return Update(_MyDBEntities.Men.Single(p =&gt; p.ManID == idToLookFor), newName);
}

public DbResult Update(Man person, string newName)
{
    try
    {
        person.Name = newName;
        //saving missing?
        return DbResult.Success("Record updated");
    }
    catch (Exception e)
    {
        return DbResult.Failed(e.ToString());
    }
}


And the real saving missing or it's placed to elsewhere so why are you setting here the DbResult?