the two main ones are ethenylbenzene or phenylethene.
they basically mean the same thing its just a case of what u define to be the main group i.e. do you define it as the ethene part, then the other hexagon bit becomes a side group/alteration to the regular structure.
This is the case for phenylethene because the main structure is defined as ethene then this leaves us with a benzene ring that has one hydrogen missing, so therefore we call it a phenylethene.
in the other name we define the benzene bit as the main group and therefore the other bit will be the double bond version of an ethyl group which is an ethenyl group i.e. giving ethenylbenzene