Hm?
The standard, nominative form of the name in Middle Irish was
Sitriuc, whereas
Sitric is modern and in the genitive case.
As for his byname, here is part of the paradigm:
árchú ‘warhound’
int árchú ‘the warhound’
árchon ‘of warhound’
ind árchon ‘of the warhound’
Old and Middle Irish bynames
need no definite article (i.e. no equivalent of 'the'), so Sitriuc the Warhound is simply
Sitriuc Árchú, just like Áed the Black (i.e. Black Áed) is simply
Áed Dub.