"Jubilate deo Jacob" is translated everywhere as "rejoice unto the god of Jacob". But from what little I know, Jacob is not in the genitive case. May I ask if this was a grammatical shift when in ecclesiastical Latin, or that Jacob is taken as genitive in specific context.
To add a little context to the current answer, the name "Jacob" in the New Testament has two distinct forms:
- Ἰάκωβος/Iacobus, which is declinable
- Ἰακώβ/Iacob, which is indeclinable
Iacobus is used to refer to the apostle James, while Iacob refers to the Old Testament patriarch Jacob. I'm not sure why the two names were distinguished this way, since (as far as I am aware) they are the same Hebrew name.
In your quote, "Iacob" is used in the second, indeclinable way because it refers to the patriarch, and the genitive makes the best sense in context.
Matthew 27:56 offers an interesting example of a declined "Iacobi" (referring to the apostle). It's especially interesting because it is paired with another name that isn't declined: "Ioseph":
...inter quas erat Maria Magdalene et Maria Iacobi et Ioseph mater et mater filiorum Zebedaei.
...among whom was Mary Magdalen and Mary, the mother of James and Joseph, and the mother of the sons of Zebedee.
The name Jacob not a Latin or Greek name and it is not clear how one should decline it to other cases like the genitive. The choice made with many biblical names that do not fit pre-existing patterns is to treat them as undeclinable. The nominative, accusative, genitive, dative, ablative and vocative are all Jacob.
Thus in this context Jacob is indeed a genitive. But you can't tell it by looking at the word as all cases look alike, you can only tell it by context. This makes these words difficult to parse if the grammatical construction is complicated, but in relatively simple cases you can still parse it with some ease — at least if you know to expect that Jacob could be any case.