A formal Irish name consists of a given name and a surname. In the Irish language, most surnames are patronymic surnames (distinct from patronyms, which are seen in Icelandic names for example). The form of a surname varies according to whether its bearer is a man, a woman, or a woman married to a man, who adopts his surname.

An alternative traditional naming convention consists of the first name followed by a double patronym, usually with the father and grandfather's names. This convention is not used for official purposes but is generalized in Gaeltachtaí (Irish-speaking areas) and also survives in some rural non-Gaeltacht areas. Sometimes the name of the mother or grandmother may be used instead of the father or grandfather.

A first name may be modified by an adjective to distinguish its bearer from other people with the same name. Mór ("big") and Óg ("young") are used to distinguish parent and child, like "senior" and "junior" are used in English, but are placed between the given name and the surname, e.g. Seán Óg Ó Súilleabháin corresponds to "John O'Sullivan Jr." (anglicised surnames often omit ⟨O'⟩, leaving no trace of original Ó).

The word Beag ("little") can be used in place of Óg. This does not necessarily indicate that the younger person is smaller in stature, merely younger than their parent or in some cases to imply a baby was small, possibly premature, at birth.

Adjectives denoting hair colour may also be used, especially informally, e.g. Pádraig Rua ("red-haired Patrick"), Máire Bhán ("fair-haired Mary").

Colloquially in Gaeltachtaí (Irish-speaking areas) and some other areas it remains customary to use a name formed by the first name (or nickname), followed by the father and the paternal grandfather's name, both in the genitive case, e.g. Seán Ó Cathasaigh (Seán O'Casey), son of Pól, son of Séamus, would be known to his neighbours as Seán Phóil Shéamuis. Occasionally, if the mother or grandmother was a well-known person locally, her name may be used instead. If the mother's name is used, then the maternal grandfather or grandmother may follow it, e.g. Máire Sally Eoghain.

This system can be particularly useful for distinguishing people who live in the same area and who share a common surname but are not closely related, e.g. two people named John McEldowney might be known as "John Patsy Dan" and "John Mary Philip" respectively. Even the Irish forms sometimes survive in parts of the Sperrins, so that among the principal families of Glenullin some branches are known by father/grandfather forms such as Pháidí Shéamais or Bhrian Dhónaill.

A man's surname is generally formed by Ó ("descendant"; historically Ua) or Mac ("son") followed by a name or definite noun (often a profession) in the genitive case, e.g. Ó Dónaill (literally "descendant of Dónall") and Mac Siúrtáin (literally "son of Jordan"). When Ó is followed by a vowel, a (lowercase) ⟨h⟩ is attached to the vowel, e.g. Ó hUiginn (O'Higgins) or Ó hAodha (Hughes).

A woman's surname replaces Ó with Ní (reduction of Iníon Uí "descendant's daughter") and Mac with Nic (reduction of Iníon Mhic "son's daughter"). In both cases the following name undergoes lenition, except for when Nic is followed by ⟨c⟩ or ⟨g⟩. Thus the daughter of Seán Ó Dónaill has the surname Ní Dhónaill and the daughter of a Pól Mac Siúrtáin has the surname Nic Shiúrtáin. In Ulster it is common for a woman who adopts her husband name to just use Ní or Nic rather than the forms seen below.

If a woman marries a man, she may choose to take his surname. In this case, Ó is replaced by Bean Uí ("descendant's wife") and Mac by Bean Mhic ("son's wife"). In both cases Bean may be omitted, which results in Uí or Mhic. In both cases the following name undergoes lenition, except for when Mhic is followed by ⟨c⟩ or ⟨g⟩. Thus a woman marrying Seán Ó Dónaill may choose to adopt Bean Uí Dhónaill or Uí Dhónaill as her surname and a woman marrying Pól Mac Siúrtáin may choose to adopt Bean Mhic Siúrtáin or Mhic Siúrtáin as her surname.

Mag, Nig, and Mhig are sometimes used instead of Mac, Nic, and Mhic before a vowel or ⟨fh⟩ (which is silent) followed by a vowel.

Norman surnames formed by de (always lowercase; "of") followed by a name, e.g. de Búrca (Burke), de Paor (Power), or de hÍde (Hide, Hyde).

Some names consist of Mac Giolla ("servant's son") or Ó Maoil ("follower's descendent") followed by a name in the genitive case, e.g. Mac Giolla Phádraig, Ó Maoil Eoin.

Many Irish people use English (or anglicised) forms of their names in English-language contexts and Irish forms in Irish-language contexts. The Irish names of some people more famous under their English names include:

Other people are generally better known by their Irish name than by their English name, including the following:

• List of Irish-language given names
• Celtic onomastics
• Place names in Ireland
• Scottish Gaelic name
• Welsh surnames

• Names - Nualeargas
• Irish Names at LibraryIreland.com
• The Origins of Irish Surnames at IrishTimes.com (Archive)
• Find Irish Family Names at Dubliner.com
• 16th & 17th Century Anglicized Irish Surnames from Woulfe by MedievalScotland.org