Tor, originally from "The Onion Router", works by routing your traffic through multiple Tor nodes. Like an onion, each node only peels off one layer and passes the packet on to whoever is addressed on that layer. Each node only knows the details about the next node. Eventually, the packet will hit an "Exit-Node", at which point it will be routed via the internet through the endpoint, but it's not a single route.
And while that does not change for every request (that would be highly unpractical), all Tor clients offer you a very quick "get a new route" with just one click.
Just to clarify, it's Tor clients that select which relays (entry guard, middle and exit) to use in circuits. Also, each relay in a circuit knows (or at least, could know, if it wanted to) both source and destination. But with three-relay circuits, no relay know both user identity and destination.
Also, by default, Tor changes circuits at 10-minute intervals.
And while that does not change for every request (that would be highly unpractical), all Tor clients offer you a very quick "get a new route" with just one click.