There is an English surname Bryson or Briceson (i.e. son of Brice), but in Ireland it has an Irish origin in Ulster, particularly in Counties Donegal and Derry. This is clearly indicated in its earlier anglicized forms: the seventeenth century Hearth Money Rolls for the northern counties list many householders whose name is written Mrieson and similar variants, which is an approximate phonetic rendering of O Muirgheasain. The "census" of 1659 gives O'Mrisane as a principal Irish name in the barony of Inishowen, Co. Donegal. As might be expected this has been largely absorbed by the better known Morrison. Even as early as 1606 O'Morison was not unknown in Co. Donegal, at any rate by the non-Gaelic authorities: for example Bishop Montgomery in his survey of the Diocese of Derry called the erenagh of Clonmany - in Inishowen Donatus O'Morison. Nevertheless Bryson is the modern form adopted and usually retained in the counties mentioned above. Woulfe states that it has become Price in Co. Mayo; but of course this is normally a Welsh name (viz. Ap Rhys). Price is a very numerous name in Ireland, found in all the provinces and on record since early mediaeval times.
Coats of arms:
There are no coats of arms on record for Mrieson or O Muirgheasain For Bryson we find Ref. 139/65 Bryson (Craigton, Scotland) Arms: Gules a saltire between two spur rowels in fesse a spearhead in chief argent and a crescent in base or. Crest - a hand holding a horn proper. Motto - vivit post funera virtus. Given the interchange between Ulster and Scotland, this might relate to a family with origins in Donegal or Derry, though it must be said that the saltire is a very Scottish heraldic symbol.
Ref. 139/66 Bryson (no location recorded) Gules a saltire between two spur rowels in fesse a spearhead in chief argent and a crescent in base or. Crest - a ship under sail. Motto - God with my right. There are several Morison coats of arms on record in Scotland. There is nothing to indicate that any are or Irish origin.
There are several Morrison coats of arms on record in Ireland. None are recorded as belonging to Donegal or Derry.