Well, they are all correct but have slightly different meanings:

The user cannot be identified clearly.
The process of identification is the problem.

The user cannot be clearly identified.
The problem is the identification of the user.
(This is the one I would use)


The user cannot clearly be identified.
This one could be wrong, actually. There's something bugging me about it I can't put my finger on.

I also think the third option sounds strange.
I it's because the adverb should be next to (before or after, depending on the meaning) the main verb and not the auxiliary. The reason being that the adverb is used to define the main verb and not the auxiliary verb.

Here's one more:

The user clearly cannot be identified = It is obvious that this identification is impossible

The third option is definitely wrong.

Building on Netzspannung's and Robert's postings, let's look at the following sentences:
(1) The user is identified clearly.
The process of identification produced a positive result.
(2) The user is clearly identified.
There is no doubt about the user's identity.
(3) The user clearly is identified.
This makes sense only if the auxiliary verb is meant to be stressed, i.e.,
(3') The user clearly is identified.
This ascertains the fact of the user's identification, perhaps in response to some challenge. The construction is similar to an adverbial modification, e.g., 'The third option definitely is wrong'. Now introduce another negated) main verb:
(4) The user cannot be identified clearly.
(5) The user cannot be clearly identified.
These are perfectly fine constructions similar to (1) and (2). The construction
(6) The user cannot clearly be identified.
is wrong since 'cannot be' may only be adverbially modified as a whole, similar to (3), leading to Robert's perfectly legitimate sentence:
(7) The user clearly cannot be identified.