I always refer to them as Hennes as that's what they started as, maybe in the 80s. Poss. the chain needed a cash injection from a partner and it was renamed. The full names would be a mouthful for shoppers.
The chain used to be called just 'Hennes'. I expect an injection of money was needed via a new partner. As the two names are a bit of a mouthful for shoppers I reckon they thought up the more snappy 'H&M'.
"Mauritz came from the name of the Hunting andGun shop Mauritz Widforss in Stockholm. Hennes took over the shop in 1968 and Mauritz was added to the company name.