There is too much historical naming convention using "json" in names; and this is particularly unfortunate at databinding level where multiple other formats are supported.
With 3.x we can start improving on at least some of these cases.

One initial thing to do for 2.13 would be to add new DatabindException as base type of JsonMappingException (similar to StreamReadException (under JsonParseException) and StreamWriteException (under JsonGenerationException)) -- for 2.x it can be used as receiver (but not thrown), and for 3.0 we can start actually using it and possibly remove JsonMappingException.