The coverageName parameter is ignored when creating an external ImageMosaic through the REST API. The name of the resulting layer is set to the name of the enclosing directory. I am specifically working with database backed ImageMosaics, so I am not sure if this is also an issue with shapefile backed mosaics. The same URL with external.imagemosaic substituted with external.geotiff for instance works as expected. I am setting "content-type" to "text/plain" and "accept" to "application/xml" in my requests.
results in a CoverageStore named "mosaic" and a layer named "mosaic" rather than a layer named "layer"
results in a CoverageStore named "mosaic" and a layer named "layer as expected.
CentOS 7 with Oracle JRE 1.8.0