Edit: After a chat with Richard, it seems like tag synonyms are a bad solution for the structure I was imagining. This would completely remove the utility of the individual books.
Tag usage and consistency is a problem across all SE sites. Admittedly, many of the questions tagged as old-testament or new-testament would be better served using different tags. However, I don't think that we should get rid of these tags on this basis.
There are valid questions that are exclusive to the old testament (for example). Furthermore, the old-testament tag is useful to indicate that the answers should focus on the old testament rather than the new.
Ultimately, the usage of these tags has been questionable at best, I agree. We should edit the questions that are inappropriately using these tags to correct the tag usage.
I don't think we should make individual books synonyms of the half of the Christian Bible that they are a part of.
There could be very valid questions regarding the book of John, for example, that should have it's own separate section (and therefore it's own separate tag). Furthermore, there are books that are non-canonical but would be on-topic for this site, I believe. These books would fall outside of the "old-testament" and "new-testament" tags.
So, I think we should leave them all separate, allowing for both the testament tags as well as the book-specific tags.
I think there should be a tanakh tag which ought to be used for questions purely about the Hebrew scriptures from a Jewish or neutral perspective. It is a synonym for old-testament except for those Christians who include the apocrypha in their Bibles. I've retagged the questions that I think already fall under that category and I think it goes a long way toward making this cluster of tags useful.