Usage
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.
Synonyms
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.