Now that the tune is the top one, I can play it. I agree with Open Mike that it sounds modern. Well, modern as opposed to a Playford dance from the 17th or 18th century, anyway.

If you don't get an answer, I suggest you give it one of those traditional names such as

Jackie's Favorite
Jackie's Delight
Jackie's Fancy or

if you want to sound Irish, just plain 'Jackie Allen's.'

I enjoyed listening to your playing.
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I know a beautiful Welsh tune called 'Conset Argyllwth Treffael.' People insisted that 'Conset' didn't make any sense. Eventually I learned that is a Welsh-English form of 'conceit.' But I wouldn't suggest calling it Jackie's Conceit.