Hello. We are looking for car service recommendations for 8 people with 8 suitcases to travel from Rome to Positano (2 hour stop in Pompei). Does anyone have any companies that are reliable and reasonable? Thanks!

You may have to redefine reasonable. This will cost several hundred Euros, and will require a company with a large vehicle, if not two, for that many people and luggage. I have been pricing a car transfer from Rome to Naples for two, and have gotten quotes ranging from 300-450 E. I would also suggest posting this question at TripAdvisor, and doing a Google search for companies. If you are staying in a hotel in Positano ask them for a recommendation.

Last time I checked it was 400 Euros Rome to Positano with private driver in a normal size car.. But you need a larger vehicle so probably more expensive.
Or take the train Rome to Naples and then a driver service to Positano.

Try Tiber Limo- I know they can accommodate 8 persons with luggage. We used them a few years ago from Amalfi to Rome with good results.

Tiber Limousine Service - Limo service in Rome & Italy

I think, but I am not positive, that fees are set by the taxi cooperatives, so I am not certain that you should waste time pricing out various options. One driver may be much better than another as far as personality and driving skills, and English capability, but I am not sure you will save much by going from one to another. At least that has been my experience on several trips to that area.
Your best chance for a lower price might be to book just before you want to travel; we did this and on the spur of the moment got a very slightly lower price for travel to and from Sorrento to Amalfi coast towns. Booking in advance might mean booking at the set price, higher possibly than booking at spur of the moment. But again, I never traveled by taxi as far as Rome; that's a big price committment but maybe ok when shared with a few others, based on your budget.