Riall, O Ragaill, O Raogail

Origin is Irish where it is usually found as Rahill, Real and Ryall. In general the name is found in County Cork 
where it is believed to be a derivative of O'Rahill and O'Reale. The name is indeed a derivative of O'Reilly.

http://www.ucc.ie:8080/cocoon/celt/G100013

Mac Carthaigh's Book

Miscellaneous Irish Annals (A.D. 1114-1437)

Fragment I

(Nat. Libr. Irel.MSS. No.6, fos.1a-12b; No. 5, fos.9a-24b)

Anon

entry MCB1126.8 

h-Ragailligh

Woulfe's Sloinnte Gaedheal is Gall (Irish Names and Surnames) offers the following explanation on the Ryall
and Rial surname: 

O Raghaill - I - O Raghell, O Reile, O Ryle, O Reale, O Raile, O'Rahill, Rahill, Reihill, Ryle, Ryall, Rall, 
Rail, Riall, Real, Reel &c.; a shortened form of O Raghallaigh, q.v.; sometimes also pronounced O Raghaill, 
O Raighill, O Ra/ighill, O Raoghaill, O Reighill &c. 

O Raghallaigh: 

O Raghailligh, O Raghallaigh - I - O Reyly, O Riellie, O Really, O Reely, O'Reilly, O'Reiley, O'Rielly, 
O'Realley, Reilly, Rielly, Really, Realy, Reely, Riley, &c.; "descendent of Raghallach"; also pronounced 
O Raghallaig, O Raighilligh, O Raghaill &c., q.v. The O'Reillys, who are the same stock as the O'Rourkes, 
were chiefs of Breifney-O'Reilly, which originally comprised the greater part of the present Co. Cavan. 
In the course of the 13th and 14th centuries they became very powerful and extended their dominion over the 
whole Co. Cavan and parts of Meath and Westmeath; and they were sometimes chiefs of all Breifney. 
They maintained their independence as a clan down to the time of James I, and continued in possession of 
considerable property until the Cromwellian confiscations. Many of the O'Reillys attained to high ecclesiastical 
rank, no fewer than five of the name having been Primates of Armagh. The name is now one of the most common 
in Ireland, but owing to its numerous dialectical variations is variously anglicised in different parts of the country. 

MacLysaght, The Surnames of Ireland, (Irish Academic Press, 1964): 

Riall - See Ryle 

(O) Ryle, Riall 

Woulfe gives the form in Irish as O Raghaill and considers this to be an abbreviated form of O Raghailligh, 
O'Reilly which is conjectural: its equation with the Kerry Rahilly would seem possible. Ryle is the usual 
spelling in Kerry, where the name is mainly found. See Rahill and Reighill. 

(O) Reighill O Raghaill, now often O Reighill. A Fermanagh name also called Reckle there. Rehill, Reehill and 
Rahill are variants found in Cos. Longford and Cavan.