This has mostly been answered in the comments already, but I'll summarize and throw in my own interpretation as well. There are two things going on which might be causing the uncertainty, though the original guess is correct in that it should be ''den''.
First, ''nennen'' has an unusual valence in that it takes a subject, an accusative object, and a predicate which can be another object. When a predicate is a noun then it has to have a case, and in German that case matches the case of the noun that it's being compared to. For example:
Ich bin der König. ― "I'm the king." (der König takes the same case as ich.)
Man nennt mich den Meister. ― "They call me the master." (den Meister takes the same case as mich.)
This is very logical but a bit confusing for English speakers because when the predicate is a noun in English it takes the objective case (aka. the oblique case) just like any other object. So "It's me," rather than "It is I," at least for most speakers. (I've heard the phrase "This is (s)he," used in phone conversations, but usually in old movies where the speaker is using a Mid-Atlantic accent. It may be "proper" but no one I know speaks that way naturally.) The upshot is that, at least in a main clause, you'd use the accusative case for the direct object and the predicate:
Wir nennen ihn den modernen Kriminellen.
The other issue is whether the relative pronoun takes its case from the clause it introduces or whether it matches the noun it refers to in the main clause. Again, English speakers don't have much intuition for this because "whom" is gradually disappearing in favor of "who". (To my ears, "whom" only sounds correct after a preposition: "For whom the bell tolls," but "Who are you going to call?" Perhaps this is inconsistent, but it's the kind of thing you have to expect when the accepted grammar is in a state of flux.) As for the previous issue, it helps to construct simpler examples. The upshot is that the relative pronoun takes the same case in a subclause as it would have if it was a main clause. For example:
Ich habe ihn gestern gesehen. ― "I saw him yesterday."
Karl, den ich gestern gesehen habe, ruft mich an. ― "Karl, who I saw yesterday, is calling me."
Ich habe ihm gestern ein Buch geliehen. ― "I lent a book to him yesterday."
Karl, dem ich gestern ein Buch geliehen habe, gibt es zurück. ― "Karl, to whom I lent a book yesterday, is returning it."
Putting these ideas together, the criminal would take the accusative case if it was a main clause, and this doesn't change when it's turned into a relative clause, so he remains the accusative ''den''. Sometimes German grammar isn't quite as logical as one might hope, so this kind of reasoning doesn't always work, but there don't seem to be any exceptions that apply in this case.