Using the genitive case, you would get “In ainm Dé ghrástúla, thrócairigh”, which is grammatically correct, but doesn’t sound very natural, so I would rather suggest “In ainm Dé atá grástúil agus trócaireach” (In the name of God who is graceful and merciful). Still, I’m not a native speaker nor well versed in religious terms, so I would wait for more comments. As regards Fachtna, in Modern Irish the genitive case of personal names is formed simply by adding “h” to the initial consonant, so that “Fachtna’s house” would be “teach Fhachtna”.