Is it the denomination of the PhD course very important? I received an unconditional offer for a PhD from two different universities. The first from a famous Department of English. The second from an average Department of Comparative Literature. (I have an MA in Comparative Literature and have studied Russian and English).

My research proposal - for which I received an offer in both departments – has, however, a multi-national and theoretical approach. I was wondering: if I accept the offer at the Department of English, will I still be able, after graduation, to apply for a post-doc position in Comparative Literature? Clearly, I wish to publish papers in Comparative Literature and write my PhD dissertation with a comparative approach.

P.S.: I don't know if this information is necessary, but I am an Italian student and got both my BA and MA in Italy.
No, the name of your degree is not important in most cases. You will be judged based on the quality and area of your work and research and your publication record. If you publish with a comparative approach and want to do a post-doc in a comparative department, you won't be impeded simply because your degree says you have a PhD in English.

It is more important that you have an advisor (and perhaps other mentors as well) around you that can assist you in the approach you wish to take. If no one in this Department of English has any expertise in a comparative approach (I think it would be highly unlikely that no one would, but perhaps no one you were interested in working with), that's a bigger issue than the name of the degree, and something you should actually consider.