There are two prominent Macartney Coats of Arms. The first is, or rather was that of Lord George Macartney (1737-1806). He was knighted in 1764 before going to Russia as Envoy Extraordinary. Likely this is when he commissioned his Arms. Macartney used a stag surmounted by a helmet from the top of which projected a hand holding a single rose. The motto was "Mes conscia recti" or "A mind dedicated to the right things". He and his descendants were entitled to use the Arms but as he died without issue the Arms died with him. Other family members (or anyone else) would not have had the right to use his Arms.
Another Coat of Arms was devised for Sir John Barrington Macartney, 6th Baronet of Nish (possibly Lish), Co. Armagh. This is somewhat similar, though less elaborate, than George's and the hand holds a spray of three roses. Other Macartneys who did not have a personal Coat of Arms simply used a crest consisting of a hand holding one or more roses in various configurations.
What has happened in recent years is that people interested in family history have been conned by commercial interests who sell crests of various families. People with the same name imagine the crests are their rightful crests just because of the name.
While it is not illegal, it must be recognised that family coats of arms were drawn up for an individual noble (i.e. wealthy or important) family and just because you have the same name does not mean that it is also your coat of arms. Many coats of arms were Victorian creations to please families who have risen to wealth and power and are often as contrived as the tartans which also, were often designed in Victorian times when Queen Victoria had a passion for all things Scottish. Some Irish arms and Scottish tartans may be authentic but most, more often than not, are merely Victorian nonsense.
In point of fact the right to have a coat of arms is given to a particular person and may be inherited by the family. However persons with the same name who are unrelated cannot rightfully use it, although many do. So unless your family were given a coat of arms by the Irish College of Heralds it is improper to claim someone else's as your own. In the tourist shops you can buy a crest of any family but everyone with the same name is really not entitled to display it as that of your family. Unless one is a direct descendant of the original owner of the Arms it is not proper to use them as one's own. It is perfectly all right to use any form of a hand holding one or more roses as a crest I think but it should not be miss-labeled as a Coat of Arms.
The Macartneys/McCartneys who came back to Ulster from Galloway, Scotland, starting about 1610 represent most of our ancestors. They were poor tenant farmers for the most part - peasants, in fact, and if you had asked them about their family crest they would have laughed because only noblemen had such things. I am afraid those who peddle so-called Coats of Arms to people seeking their roots are rather unscrupulous and are mostly making the designs up or are taking the personal Arms of noblemen with whom few of us have any direct connection. These noblemen were themselves once farmers but managed to rise in the financial and social scale receiving knighthoods for service to the crown or a promise of allegiance.
The important McCartneys in Ulster are mostly descended from three well-to-do Scottish Ayrshire landowners who became famous and wealthy in early Belfast. A few were knighted and naturally wanted a coat of arms to go with their position. Thus there are several versions of arms associated with these families. However most McCartneys/Macartneys who settled in Ulster in the early 1600's had the same name as the landowners but were dirt poor farmers and their relationship with the important families was extremely remote.