There is no regulation for common names like there is for scientific names, of which there is only one per plant that is correct at any given point in time. The nearest I can think of at the moment to check what is the "correct" common name in this case, FWIW, would be the cultivar registration authority for Lagerstroemia, which is the United States National Arboretum. They call it crapemyrtle, all one word:
http://www.usna.usda.gov/Resea...
Edit: ITIS (Integrated Taxonomic Information System) also goes with the one word crapemyrtle:
http://www.itis.gov/servlet/Si...
However, TROPICOS (Missouri Botanical Garden) quotes a 1995 book "Scientific and Common Names of 7,000 Vascular Plants in the United States" to justify "crape-myrtle" with a hyphen as the English common name. Either way it seems these authorities prefer the a spelling rather than e.
http://www.tropicos.org/Name/1...
Sorry for not italicizing where it should be, but I'm fairly new here and would need to go and look at the code for that and might lose the post.
