Question is: Without hamburger, does it cease to be 'Hamburger Helper' and become merely 'Helper'?
I say yes. It is possible to judge people with this question.
Before the invention of the other Helpers (ie; chicken, tuna, etc), I think saying it stayed H.H. would have been acceptable. But now that there are multiple Helpers, I think that once the Helper doesnt have it's required item its supposed to be helping, it ceases to be that item's helper and is simply Helper itself.