To get the field always use the GUID it's the safest. And always put it into a local variable to work with:
var field = customersList.Fields[SPBuiltInFieldId.Title];
To change the display name on the main language (and depending on your settings force that down on all the other languages) set the Title attribute and call Update on the field:
field.Title = "My New Title";
field.Update();
To change the MUI version of the display name on a secondary language user TitleResource.SetValueForUICulture:
field.TitleResource.SetValueForUICulture(new CultureInfo("nb-NO"), "Local Title");
field.Update();
And to annoy everybody this only set the local display name for one of the three Title fields so you have to repeat it for the other two:
field = customersList.Fields[SPBuiltInFieldId.LinkTitle];
field.TitleResource.SetValueForUICulture(new CultureInfo("nb-NO"), "Local Title");
field.Update();
field = customersList.Fields[SPBuiltInFieldId.LinkTitleNoMenu];
field.TitleResource.SetValueForUICulture(new CultureInfo("nb-NO"), "Local Title");
field.Update();
So the total sequence may be something like:
var field = customersList.Fields[SPBuiltInFieldId.Title];
field.Title = "My New Title";
var culture = new CultureInfo("nb-NO");
field.TitleResource.SetValueForUICulture(culture, "Local Title");
field.Update();
field = customersList.Fields[SPBuiltInFieldId.LinkTitle];
field.TitleResource.SetValueForUICulture(culture, "Local Title");
field.Update();
field = customersList.Fields[SPBuiltInFieldId.LinkTitleNoMenu];
field.TitleResource.SetValueForUICulture(culture, "Local Title");
field.Update();