On most insurance comparison sites, my z1000sx comes up as a H2.
Usually you can pick a menu with options and lists of bikes, and pick your bike from list.
I went with Bennett’s in the end, rung them and they had it as H2 as well, the telephone handler went through the options list with me over the phone and we found the correct bike, no problem. Interestingly they don’t have the WJF model on the their list ( or they didn’t then, we will see this year at renewal)
No need to run.