How Did The Surname Noble Arrive In Scotland?

I'm not quite sure how the name of Noble came to Scotland. I am presently researching my family tree and have a William Noble born in 1666 and living in and/or around Biggar.
According to research done by my father, there is a record of a Peter Noble living in Warwickshire in 1155. A Robert le Noble is mentioned in the Curia Regis Rolls as living in Huntingfordshire around 1206. The Hundred Rolls mention a Hugh le Noble living in Bedfordshire in 1273.
One theory is that the name Noble came originally from France in the form of le Noble, Literally meaning one of noble bearing.
My family tree starts with William Noble (1666) who married a Christian Dobie and had with her 10 children.

If this information is of use I would be pleased to exchange further details.

The surname was probably introduced by an English family of this name who settled in East Lothian at the end of the twelfth century.
They were sub-vassals of the de Vallibus or Vaux family and had the name Nobilis.
William Nobilis held part of the lands of Garmilton under William de Valibus.
A Radulphus Nobilis witnessed a grant by Vinianus Mulineys to the hospital of Soltre 1198 - 1234.
A family name Nobill held lands in Dunbartonshire in the seventeenth century. Alan Nobil was a tenant in the Barony of Stobo in 1512.
A Patrick Nobill had a remission for his part in holding the castle of Dunbarton against the king in 1489.
Thomas and Patrick le Noble rendered homage in Edinburghshire in 1296.

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