In Episode 3: Bushwacked, Mal freely admits to his identity as Malcom Reynolds, former browncoat Sergeant. His crew and passengers also freely admit to their identities.
Later, in Episode 5: Safe, Mal docks with an Alliance Cruiser to request that they save Shepherd Book's life. In this case, he gives the officer forged paperwork under a different name. The officer looks over the paperwork and says:
Official seal's out of date, Captain... Harbatkin?
Logically, this seems backwards: he admits to his identity when he's committing an actual crime, and hides it when he's innocent and just requesting medical aid.
Why the change?
Was the first encounter some sort of "honesty attempt" that didn't work out the way he expected? So he decided to play it safe from then on?
Was the real Captain Harbatkin somehow related to the Alliance, and thus might be more likely to get the medical help they were seeking?