Kaiba (award-winning animé; weird visuals that ultimately emphasise the underlying theme; all about memory and identity)
Eclipse Phase sourcebooks (tabletop RPG, the most coherent treatment of this kind of thing I've ever seen; open-source)
From the New World (animé again; further future and more fantasylike than cyberpunk, but very much about what it means to be human)
Someone has already mentioned Rainbows End
Chasm City by Alastair Reynolds (novel, further future - part of a wider series but this one has particular identity aspects to it. Can be a bit long and cumbersome - try Diamond Dogs for shorter Reynolds, though that's further detached from present reality)
Altered Carbon (and sequels) by Richard Morgan (novels (the first one in particular has a whodunnit aspect), near-future, about memory and identity, written from a fairly leftist perspective about a capitalist dystopia)
Various of Jon Courtenay Grimwood's novels, particularly 9tail Fox. Grimwood is... divisive, and sometimes hasn't done the research, but it's very much this kind of subject matter
Possibly Carlucci by Richard Paul Russo (novel with a police side, very much grounded in San Francisco - I can't remember this so well)
This is not the kind of question you can say "why not?" about. I simply didn't find Akira that thought-provoking, and I'm not aware of it having anything interesting to say about identity.
Eclipse Phase sourcebooks (tabletop RPG, the most coherent treatment of this kind of thing I've ever seen; open-source)
From the New World (animé again; further future and more fantasylike than cyberpunk, but very much about what it means to be human)
Someone has already mentioned Rainbows End
Chasm City by Alastair Reynolds (novel, further future - part of a wider series but this one has particular identity aspects to it. Can be a bit long and cumbersome - try Diamond Dogs for shorter Reynolds, though that's further detached from present reality)
Altered Carbon (and sequels) by Richard Morgan (novels (the first one in particular has a whodunnit aspect), near-future, about memory and identity, written from a fairly leftist perspective about a capitalist dystopia)
Various of Jon Courtenay Grimwood's novels, particularly 9tail Fox. Grimwood is... divisive, and sometimes hasn't done the research, but it's very much this kind of subject matter
Possibly Carlucci by Richard Paul Russo (novel with a police side, very much grounded in San Francisco - I can't remember this so well)