I've previously been a bit harsh on Matoko Shinkai. Your Name doesn't abandon the romantic longing of 5 Centimeters Per Second, but the angst is worn more lightly, and the characters feel less like ciphers. The animation is also more restrained – the night skies no longer look like Rainbow Road in Mario Kart, and there is a rather cool dream sequence which swaps crisp photorealism for a more flowing, sketched style.
The plot, as with many a time travel story, breaks apart the more you prod at it. But the conceit of two teenagers switching bodies is employed well. Shinkai has said that some of the town vs country stuff comes from his own experience of growing up. More important for me, however, is the way inhabiting another person's life becomes a metaphor for falling in love. Because being in a relationship is sort of like that. You gain access to memories of things you didn't experience at first hand. You learn about a childhood different from your own, with a new family and set of friends. You also get to know someone else's body in intimate detail (a source of some of the film's funniest moments). And by becoming comfortable in each other's skins, the two characters find that they cannot live happily without each other.
This is eked out a bit in the final part of the film, where Shinkai contrives to separate his heroes, and have them morosely wander around Tokyo searching for their other halves. But it serves to highlight how draining the loss of such a person might be, and it leads to a very satisfying finale.