What's in a name:Cornu,Helix,Cantareus or Cryptomphalus?

There is no snail more well known than Helix aspersa,but should you use this name at all?Because there is also no snail 
with so many different names than Helix aspersa.
The genus name Helix has been used for centuries,in the beginning of snail systematics the number of snails in the genus Helix was very large.
Originally almost all the snails now in the family Helicidae were named Helix,for example Helix nemoralis.
Later,when the knowledge of anatomy became greater,they were placed in their own genera.
This cleared up a lot of the confusement in the naming of snailspecies.However there was
one species that seemed to be having a sort of identity crises:Helix aspersa,and lets use this name for now.
To try to make it understandable lets start at the beginning.In 1778 Born named the snail
Cornu copiae,the illustration shows the shell to be a scalariform example of Helix aspersa
Muller,1774 however.And the ICZN(The International Commission on Zoological Nomenclature) rules dictate that names based 
on deformed specimens are not valid.
Unless the person giving the name was not aware of it being a deformed specimen thinking
it was a normal example of the species in which case it is a valid name.
Then there are the names Cantareus Risso,1826 and Cryptomphalus Charpentier,1837.Cantareus is a name rarely used for Helix aspersa,instead 
it is a subgenus for Helix(Cantareus)aperta Born,1778.Cryptomphalus aspersus as a name
can be found regularly used too,so the question is which name should we use?
Well as long as the ICZN hasn't made a ruling yet you can use whatever name you want really.You might feel Cornu should be a genus instead of a subgenus,or Cantareus aspersus
should be the right name.
Helix aspersa however is still very widely used,although that is just the name most malacologists
feel is an incorrect one.
On this site I will use Helix(Cornu)aspersa,keeping Helix as the genus.