>>> Siur ríg nime,
>> Siúr rígh nimhe
> I am assuming the "S" in Siur is broad?
No, it's slender. OI follows the spelling rule
in most cases, so that words beginning si- or
se- are pronounced /s’/ ("sh" as in "shave").
There is, however, another point of interest.
OI "siur" originally had two syllables: sïur or
si-ur. The two syllables have been retained in
Sc Gaelic "piuthar" (sister), pronounced roughly
"pyoo-uhr". (How ScG ended up with the initial p-
is another story entirely.) When the word was
later reduced to one syllable in Irish, the vowel
was lengthened as a kind of compensation ("siúr").