The following is information generally found in books about the origin of surnames.

The given name Tighearnach (Tierney) is the root name for the surnames Ua Tigheranaigh, O'Tighearnaigh, and all the variations that later became standardized as O'Tierney.  There is also a surname Mac Tighearnaigh (McTierney) however it is very uncommon.

The given name Tighearnan (Tiernan) is the root name for the surnames Ua Tighearnain, O'Tighearnain, and Mac Tighearnain, and all the variations that later became standardized as O'Tiernan and McTiernan or McTernan.

In Gaelic when there is a dot over a letter the sound of the letter is aspirated changing the sound.  This causes Mac Tighearnain (McTiernan) to become Mac Thighearnain (McKiernan).

Interestingly enough, it is very uncommon to find Ua Tighearnaigh being written Ua Thighearnaigh, and to my knowledge when it is found it is not translated as O'Kierney. 

There are several Irish surnames that are anglicized as Kearney or Cearney, but none of the reference books lists the root for these surnames as Tighearna.

Modern Gaelic makes matters even worse because in their attempt to streamline the language the historic link to Irish names has been broken.

Gaelic in Ireland and Scotland was very much the same, especially in written form until the mid-19th century.

In a current Scottish Gaelic dictionary the word is still Tighearna, but in modern Irish dictionaries the word has become Tiarna.

I have also noticed in many Gaelic language documents it is common to aspirate letters when the word is used in various tenses.

According the the Reverend Patrick Woulfe there were three O'Tierney septs.  Two were branches of the Ui Neill, the decendants of Niall of the Nine Hostages, and the other a branch of the Ui Fiachrach, founded by Niall's oldest half brother Fiachra Foltsnachtach.

According to Edward MacLysaght in "A Guide to Irish Surnames" there were three septs of the name O Tigheranaigh (Donegal, Mayo, and Westmeath) but it is now much scattered.

I designed the three faces on one head to symbolize Eocaidh Muigh-medon, the Ard Ri (High King) of Ireland (father to both), and his two sons Fiachra Foltsnachtach and Niall Naoighiallach.

Niall succeeded Eochaid as Ard-Righ and was followed by his nephew Dathi, a son of Fiachra. Dathi was stuck by lightning and killed somewhere in the Alps during his attempt to avenge his uncle Niall's death.

Flann O'Tierney, Lord of Carra (of the Ui Fiachrach in present day County Mayo), was slain by the O'Murray's in 1273 in a contest over the lordship, through the influence of Hugh, son of Felim O'Connor.  Immediately afterward Carra was taken over by the Norman de Burgos.   Some of the descendants of the former lords of Carra, particularly the O'Tierneys, may yet be traced within the barony, but most of them were reduced to extreme poverty.

As laws were passed to repress Gaelic culture in Ireland the O' and Mac prefixes were dropped in official records to make the names appear more English. 

Most Irishman were not literate in English until the mid 19th century and were unaware their names were being modified when census and land records were being recorded.

Where the person lived and the persons status determined the approximate time period when the prefixes were dropped.

Dublin and the area know as "the Pale" were the earliest areas to have Gaelic names repressed.

There was a law passed that required Irishmen to adopt the name of a colour, profession, or trade.

The surnames O'Tierney (later Tierney) and O'Tiernan (later Tiernan) were interchanged is some areas of Ireland, just like the given names.

The surname McTierney was never commonly used, however, the surnames McTiernan and McTernan are common.

McTiernan is also considered a variation of McKiernan and may not be associated with O'Tiernan or O'Tierney.

McKiernan is the anglicized form of MacThighearnain.  The aspiration makes the "K" sound.

This makes it important for people with the surname Tiernan or Ternan to know where their families originated from in Ireland, to determine if the prefix was O or Mc.

In Griffith's Valuation of Ireland (1848-1864) the distribution of Tierney families (not counting duplicate given names within a county):

Ulster = 111
Connaught = 65
Leinster = 110
Munster = 70

These numbers show a very wide distribution across Ireland for this surname.