That's going to depend on the exchange and I'm not an expert in the various trade message formats used each exchange out there, so I can't say definitively. However, as an example, CME's MDP trade execution messages do not include identifying information about the parties involved in the execution. It includes items such as order id, quantity, price, but nothing to identify a specific entity associated with the order. This is not to say that no exchanges provide identifying information. Because of how many exchanges are out there, you're going to have to provide more information about which exchanges you're dealing with if you want a definitive answer -- or to be even more sure (vs trusting some randoms on the internet), you could get the message specs for each exchange you care about and read for yourself. My guess is that for US futures and equities exchanges, the information is probably not supplied, but that's really just a guess.
Alternate trading venues, non-US assets, etc, I assume there's something out there that provides identifying info.