All Sprints from a Singular Backlog Should be Ordinal
Sprints should not be named or sequenced in anything except a strictly ordinal sense, and that's really only for release planning or burn-down purposes. A Sprint is an ephemeral time-box, and a Sprint has no life of its own once the time-box has expired.
Ideally, you should have one team per Product Backlog. If you have multiple products, you should have multiple teams. If you choose not to do that, you still need the team to work from a singular Product Backlog, and each Sprint should have a cohesive Sprint Goal. If you need to communicate about the Sprint, describe it by its Sprint Goal; don't confuse the issue by trying to track Sprint A-12, Sprint C-16, Sprint B-9, and so forth. It buys you absolutely nothing from either a framework or communications point of view.