Well if it derives from "ríoghan" like the link says it does and it's Irish then it's probably pronounced REEG-NAH or something similar. I know ríoghan would be pronounced something like REE-GAN or RAY-GAN (both are slightly different pronunciations of the name
Reagan).
Actually if you look at the name
Reagan it says it's "an Anglicized form of Ó Ríagáin meaning "descendant of
RIAGÁN"" which is similar to "ríoghan". Normally in Irish that "í" means it's pronounced like an "EE" and "á" makes an “ah” sound as in bought
Not sure if this helps any, hope it does!
*~Loads of Randomness~*
My PNLs:
http://www.behindthename.com/pnl/150423