Dinah is not the cook, dinah is dinner! its "some one is in the kitchen with dinner" the spelling it "dinah" was some person hearing the song and writting dinner phonetically. The "someone" is probably the cook who the worker on the railroad doesn't know personally. When they use dinah in "dinah won't you blow your horn" they are personifying dinner, invoking it, so to speak, to call them too it. In other words "I have been working hard all day since five o' clock in the morning and I am hungry. I wish the dinner horn would sound so I could eat... but all I hear from the kitchen is some idiot on a banjo not making me dinner." It really makes no sense any other way.