The surname Maloney or Moloney is generally Irish in origin. However there are many different variants of the name and these can include: 

Macloney, Maclony, Malone, Maloney, Maloni, Malony, Maloughney, Melaney, Meleney, Meloney, Moloney, Molony, Moloughney, Moloughny, Muldowney, Muldownie, Muldowny, Mullane, Mullaney, Mullany, Mulloghney, Mulloughney, Mulloughny, Mullowney

Based on 2014 figures, the most common variant in Ireland is Moloney, but the most common form worldwide is Maloney, with over 62,000 people bearing this particular version of the name (63% in the US).

From http://forebears.io/surnames/maloney

Irish Surname dictionaries suggest several different origins for the name and its associated variants. Woulfe (1923) gives the following:

Ó MAOLDHOMHNAIGH—I—O Malowny, O Mollowny, O Mullowny, Malowny, Molowny, Mullowney, Moloney, Molony, &c.; 'descendant of Maoldomhnaigh' (devoted to Sunday, or to the Church); the name of a Dalcassian family who were chiefs of a district in the barony of Tulla, Co. Clare; now very numerous throughout Munster. Ó Maoldomhnaigh is the same surname, but the family is apparently different.

Ó MAOLDOMHNAIGH—I—O Muldowny, Muldowney, Muldooney, Downey, Dawney; more frequently Ó Maoldhomhnaigh.

Ó MAOLFHACHTNA—I—Mullaghny, Meloughna, Mulloughney, Mologhney, Mollowney, (Mollony, Moloney); 'descendant of Maolfhachtna' (servant of St. Fachtna); an old Tipperary surname, now generally assimilated to Moloney.

In addition, the Surname Database adds:

This notable Irish surname is an Anglicized form of the Old Gaelic "O'Maoldhamhnaigh", descendant of Maoldhamhnigh, a male given name composed of the elements "mad", literally meaning "bald", but used here in the sense of "tonsured one"; hence, "devotee", and "domhnaigh", the genitive of "domhnach", (Patrician) church. The latter element "domhnach" translates as "Sunday" or "the Lord's Day" in modern Gaelic. Maloney, along with its more usual spelling Molon(e)y, is chiefly found in County Clare, and the adjoining Munster counties of Tipperary and Limerick, "O'Maoldhamhnaigh" being an ancient Dalcassian sept, that is belonging to Kiltanon near Tulla in East Clare. The "O'Maoldhamhnaigh" chief ruled over Cuiltenan in the Barony of Tulla, and his sept (along with the O'Gradys, the O'Quins and the McEneirys) is of the line of Cormac Cas, Monarch of Ireland. The name is seldom if ever found today with the original prefix "O".

O'Hart gives a description of the specific line of descent of the Maloney's in his Irish Pedigrees; or the Origin and Stem of the Irish Nation

THE O'Moloneys derive their descent from Brenan Bán, the second son of Blad, son of Cas, who is No. 91 on the "O'Brien Kings of Thomond" Stem. They were chiefs of Coiltenain (now Kiltannon), a district in the barony of Tulla, co. Clare, and had castles at Rinnua and Coolistigue. 

... Brennan Ban, ancestor of O'Brennan (of Thomond), Glinn, Glynn, Maglin, Magan, Muldowney (now "Downey"), O'Hurley, etc

So from the above, it appears that one version of Maloney is derived from the sept of the Dál gCais (hence Dalcassian). This is the "clan" that gave rise to Brian Boru (see diagram below) and it has given rise to many different surnames. The Maloney name specifically is descended from the line of Brenan Bán, and we would expect to detect a genetic connection to other surnames which are supposedly descended from this same source (namely, O'Grady, O'Quin, McEnery, O'Brennan, Glinn, Glynn, Maglin, Magan, Muldowney, Downey, O'Hurley, and many others, with or without the "O").

from www.irishtype3dna.org/surnames.php

It should be born in mind that there are many other possible origins for the name and this is just one of them. We would expect to find many different genetic signatures associated with the name Maloney. The distribution of the surname variants in mid-1800 Ireland (based on Griffith's Valuation) gives some indication of where different variants may have arisen. The majority are centred around counties Clare, Limerick & Tipperary, but there are certain variants that are concentrated in specific places, such as Mullowney in Galway & Mayo, Muldowney in Kilkenny, Mullany in Sligo & Mayo, and Mulloughney in Tipperary.

As more Maloney's do the Y-DNA-37 test and subsequent SNP marker testing, we will be able to piece together which Maloney surname variants are most closely related to each other, and we may be able to tie certain variants back to the Ancient Irish Genealogies.

Surname Distribution maps of Maloney variants in the 1850s showing total number of households in Ireland (from www.johngrenham.com)