Separate Template Name from File Name

I would like the Template Name to be separate from the file naming convention. For example: We have our Record Request document saved as Record Request but the format we name it as is: yy.mm.dd - Provider - RBF Request by Aff but when our users select it from the Template list we'd rather they be able to see it plainly as Record Request when selecting from Templates and it just show up as yy.mm.dd - Provider - RBF Request by Aff when it gets generated.