The name Tuite is of Norman origin and derived from the name de Tiúit or de Tuit.

Risteárd de Tiúit (anglicised as Richard Tuite) (ob. 1210) was the progenitor of the Irish Tuite family. He was a member of Richard de Clare, 2nd Earl of Pembroke's Irish invasion force, and Lord Chief Justice of Ireland. His part in the original invasion is acknowledged in The Song of Dermot and the Earl, which recorded his grant of land in the western part of Meath (present-day Westmeath and Longford) under the authority of Hugh de Lacy in Trim.

De Tiúit is the ancestor of those who bear the de Tiúit/Tuite surname. He is variously recorded as Tiúit, Diúit and Tuit. Numerous placenames in Meath  (Tuiterath), Cavan (Droim Thiúit/Drumyouth), Westmeath (Tuitestown in Fore; Tuitestown in Moyashel and Magheradernon, and Ballysallagh Tuite), Kilkenny (Baile an Tiúigh Thoir/Tuitestown and Baile an Tiúigh Beag/Tuitestown Little) and elsewhere are named after him and his descendants. There are two claimed sources for the Tuite surname. The first is derived from the old Norwegian words for two and one. "Tu ete". In Viking times disputes were often settled by a duel. The preferred method for measuring strength was to connect the combatants at the waist with a large belt, give them each a knife and let them fight to the finish. One can imagine a large group of Vikings shouting "two-one" at two angry Vikings - two men start - one man survives. These sorts of duels were often over a woman or livestock. Obviously the "Tuete" klan had an ancestor who appeared in these duels frequently and survived whereby the name "tuete" stuck. Even today the Norwegians and Swedish pronounce the letter "e" in the same way as English speaking people pronounce the letter "i". There is a famous statue in the "Bältespännaren parken" (the belt stretchers park) in the city of Gothenburgh in Sweden. Another suggested source is that the surname is from the Eure department of Normandy where the word "Tuit" indicates a clearing in a wooded area and is clearly the local development of the old Scandinavian placename, Thveit, brought by the Normans. Men of the North when they settled in Normandy. Even this source could be connected to the Tuete duels as these would presumably have been fought in a clearing. The surname may be from the Eure region of Normandy where the root, Tuit (generally spelled Thuit as a single or first element), indicates a clearing in a wooded area and represents the local development of the Old Norse word thveit (also written þveit), but sometimes from Old Danish thwēt, brought by the Scandinavians when they settled in Normandy^[4] and is similar to English Thwaite also from Old Norse or Old Danish.

According to a Professor Richard Coates, a placenames expert who has several articles online that mention the Tuit placenames in Normandy and their etymological ancestor in Scandinavia, the Norman placename(Tuit) could be the local development of the Scandinavian word 'thveit', which means `a space in woodland cleared for settlement and/or agriculture', ‘a clearing’. There are 5 places with this name, all spelt ‘Thuit’ and all in the Eure department.

The French prefix "de" translates to "of" and was used in geographical French family surnames. In early times it was often borne by nobles, being placed before the names of their castles or estates.

One web site (difficult to ascertain the validity) further describes the origins of the name Tuite as:

First found in Norfolk, where they held a family seat as Loards of the Manor of Thwaite near Erpingham in that shire. Originally of Le Thuit, Eure in the Canto of Les Adnelys, before the Norman conquest in 1066, Ralp del Tuit was described as "the man" of Berenger de Todeni, son of Duke Robert of Normandy. After the conquest, Ralph acquired lands from the Abbot of Holm near Erpingham, lands which he called Tuit, recorded in the Domesday Book in 1086 as Thwaite. However, the family also retained the name Tuite. In 1172 Risteárd de Tiúit (Richard la Tuite) was a member of Richard de Clare, 2nd Earl of Pembroke's Irish invasion force. He built one of the largest Motte and Bailey settlements in Ireland at Granard in 1199 and rose to become Lord Chief Justice of Ireland.

No pre-Irish records of the Tuite family have been found so far.