Having googled why wasps are called Jaspers, these are some of the theories;
The French for wasp is guêpe. The accent on the first 'e' indicates that there used to be an 's' immediately after the letter (another example is hôpital, which is French for hospital). So, if 'guêpe' used to be 'guespe', my guess is that Jasper is just a corrupted form of the old, probably Norman, French word for wasp. A 'g' in French often turns into a 'w' in English - 'guerre' becomes 'war' and 'Guillaume' becomes 'William', so jasper and wasp are basically two versions of the same word which at some point went off down slightly different developmental paths.
or
This term seems to be widespread in the southern half of England - as stated, it's used from the south west to East Anglia and also in parts of the midlands, but not in the north so far as I can tell.
No-one really seems to know its origin, "unknown but old" is about the best I can find. Very tentatively, I note that the mineral jasper is often banded and wonder if it might be something to do with this. The OED does give citations for the use of the word jasper as an adjective meaning something like "stripey", notably in the first English translation of Don Quixote (Shelton's of 1620).
or
I thought the name 'jasper' for a wasp was related to their Latin name 'vespa'.