E-ghosts are not the 'soul', but more like a digital imprint of someone who died while hooked up to the matrix. The earliest known one was Alice of Wonderland, the e-ghost of one of the original Echo Mirage hackers. She retained her memories (and one HELL of a grudge against the guy who started the Crash) to some extent. Exactly how much is unknown. Other e-ghosts are not so lucky. Especially in situations like Crash 2.0, where Jormungand was busy burning everything to the ground while JackBNimble came along to 'save' people after the fact, there seem to have been cases of degradation in the copies. Think of it like portions of the file being corrupted or unreadable. Many e-ghosts are a few sandwiches short of a picnic. A lot of them are certifiably insane.
So, not the soul of an individual. Also, it is unknown how much 'individuality' CFD personas have, as they sometimes mix with other strains, and make copies, and so on. It could be a situation like in the second and third Matrix movies, where Agent Smith copied himself into EVERYONE, and they were all Agent Smith. We just don't know.