DataTables author here - I completely agree that the API is far from the best, which is why v1.10 will include an entirely new "modern" API (with a shim for the old API to provide full backwards compatibility).
The prefix letters aren't random, but they aren't elegant either. When I first wrote DataTables I was working for a company which required the use of Hungarian notation in their coding standards, so I was trained to write that way - I've never changed it because I didn't want to break backwards compatibility. Having said that, v1.10 provides a camelCase layer, which will be what is documented at the API / options with 1.10. Again the Hungarian notation will be supported for full backwards compatibility.
v1.10 is available in github (1_10_wip branch) if you want to try it. It is pre-beta, but almost ready to roll as a beta - I just need to write the documentation.