It is said that Donald, a son of the Earl of Lennox, for his bravery in battle, had his name changed by the king to Napier. After the battle, as the manner is, every one advancing and setting forth his own acts, the king said unto them, "Ye have all done valiantly, but there is one among you who hath 'Na Pier,'" and the king gave him lands in Fife and Goffurd. The name came, however, from taking charge of the king's napery or linen at the coronation of English kings, an office held by William De Hastings, in the time of Henry I.

Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.

NAPIER. An officer in the king's bouseliold — the same as Naper, which see, A Scottish legeud, however, assigns a widely different origin. In a great battle between the Scots and some eaemj', whose nation is not specified, the former were on the point of losing the day, when one Donald, sou of the then Earl of Lennox, seized a standard, and rallied the retreating soldiers. This act of prowess changed the positions of the combatants, and resulted in the complete triumph of the Scots. The king on hearing of Donald's bravery, declared that he had Na pier — 710 equal; commanded him to assume those words as a surname ; and gave him lands in Fife, and the lands of Goffurdor Goosford. This 'mighty pretty story,' though evidently invented to explain the name, was certified to the heralds under the hand and seal of Sir Archibald Napier of Merchistoun, in 1 625. It is proper, however, to remark, that the Napiers sprang from the house of Lennox, and that their early members wrote themselves Lenox alias Napier; and it is no derogation of the dignity of this illustrious family to suppose that an earl's son, their ancestor, should have held the ofHce of Napier in the royal household.

Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.