The answer is actually "Yes, but..."
...but first, even if an employee has left under a cloud, be careful that he has not made a private agreement with HR (or his former supervisor) to keep on working as a consultant (in name only) so that he/she could get another job elsewhere as quickly as possible.
And also, this is technically the job of your HR department. So if you're not HR yourself, I'd strongly recommend that you bring this issue up to HR and have them deal with it. That's their job.
That being said, the process of flagging a former employee on linkedin is fairly straightforward.
Three clicks and you're done.
Also if we're talking about a person who's using a title he never even had in the first place (for instance, let's say he was your subordinate, but he's listing himself using your title and impersonating your role).
Then there is this form which is used for reporting fake profiles and people impersonating others.
Impersonation can be a serious thing. Not only, it can potentially tarnish the reputation of your company and potentially defraud a new employer by claiming to having worked a position that the person never had.
But impersonating a company can be the first step in preparing the ground for a more elaborate form of identity theft, social engineering, and potential fraud. After all, this person probably knows all your vendors and probably has kept all those account numbers and/or cost center numbers, and such an impersonator could do a lot of damage to your company if he/she wanted to.