If you are actually using the No Match Output of the Lookup transform:

All of the columns in the input are generally available in the output regardless of match or no match. Are you looking at a Data Viewer for the results in your example, or at some saved output like a flat file or database table. If you are looking at a saved output, then you need to change your mapping to the output file.

If you are keeping the no match in the main data stream with all the other data then you need to evaluate the values and replace them with a derived column as herladygeekedness suggests. Something like

ISNULL(LongName)?ShortName:LongName

will return the ShortName when LongName is null and LongName otherwise.