Thanks Jack. Give Me Your Hand aka Give Me Your Hand, eh?! LOL

This Wiki article says that Captain Franicis O'Neill stated that it was Latinised later rather than originally named in Latin, and I would be surprised if it wasn't first named in Gaelic:

Tabhair Dom Do Lámh

"Captain Francis O'Neill suggests

"Proud and spirited, he resented anything in the nature of trespass on his dignity. Among his visits to the houses of Scottish nobility, he is said to have called at Eglinton Castle, Ayrshire. Knowing he was a harper, but being unaware of his rank, Lady Eglinton commanded him to play a tune. Taking offence at her peremptory manner, Ó Catháin refused and left the castle. When she found out who her guest was her ladyship sought and effected a speedy reconciliation. This incident furnished a theme for one of the harper’s best compositions. 'Tabhair Damh do Lámh,' or 'Give Me Your Hand!' The name has been latinized into 'Da Mihi Manum.' The fame of the composition and the occasion which gave birth to it reaching the ear of King James the Sixth, induced him to send for the composer. Ó Catháin accordingly attended at the Scottish court, and created a sensation."