McAteer is a surname most commonly found in the north of Ireland. It is derived from the gaelic Mac an tSaoir, meaning son of a carpenter, or craftsman. Variants of the name include Mateer, Matier, McTeer, McTier, McIntyre, Carpenter, and possibly, Freeman, and Wright. 

Currently the Isles Sc/Ire 8.3 sector of the I-M223 haplogroup project has documented McAteer/McIntyre/Matier/Carpenter as DNA tested variants of the Mac an tSaoir surname. While this project evolved from the I-M223 project, and the majority of the current documented McAteers in the FamilyTree DNA database are I-M223s with origins in southeast Ulster (Armagh/Down), this project is open and welcoming to McAteers and variants of all lineages.

Some information on the name from johngrenham.com below:

Mac Ateer - líonmhar: Cúige Uladh. Tá Baile Mhac an t-Saoir in Ard Mhacha ach ní foláir go raibh an sloinne coitianta sa mheán-aois. Sa 6 céad, bhí mac an t-saoir ar Chiarán, bunaitheoir Chluain Mhic Nóis. Is sloinne Albanach é, leis, faoin leagan Mac Intyre, atá líonmhar in Ulaidh, i nDoire go sonrach. Trí aistriúchán deineadh Carpenter agus Freeman díobh, áiteanna

Mac Ateer - numerous: Ulster. Ballymacantsaoir is in Armagh but the surname must have been common in the middle ages. In the 6th century, Chiarán, the founder of Cloin MacNóis, was the son of a carpenter. It is also a Scottish surname, under the version Mac Intyre, which is numerous in Ulster, Derry specifically. By translation they became Carpenter and Freeman, places

MacAteer - numerous: Ulster generally, etc. Ir. Mac an t-Saoir, "son of the craftsman". The corresponding Scottish name is Mac Intyre, also widespread in Ulster.

Matier - Quite numerous: Down, Belfast etc. Variant of Mac Ateer.

Carpenter - fairly numerous: Leinster etc. Ir. Mac an tSaoir. Also occurs as MacAteer in Ulster and MacIntyre in Scotland.

Digital copy of Ulster Historical Foundation's 'Researching McAteer ancestors' here: https://ulsterhistoricalfoundation.com/library/mcateer-ancestors