Well, unless I am mistaken - it has been a while since I've looked at the product - the actual name
HeroQuest is being used by moon design for their rpg, set in Glorantha - as seen here:
http://www.glorantha.com/product/heroquest-core-rules/I am not sure if they still own the rights...again, it has been a good while since I've looked into them.
Personally, I would think creating a different name would be best for any group that strives for this. Using
the name HeroQuest, people will expect the same quests, and probably all of the expansions as well - I know
I would.
Using a new name, you can make your own quest packs, even if they are extremely similar to the originals,
and you can come up with your own background, setting, etc. And should it become a big hit, you wouldn't
be constrained by the original materials, you can simply add to it as much as you want.
If you redid all the original quest packs, and it was a hit seller, people might become VERY suspicious if a brand
new quest pack showed up on the market.
A new name would allow you to make sure things are nice and consistent, as well. Instead of using two different names
for the evil wizard, for example (which, no one would be able to use Zargon or Morcar anyhow - but you see my point).