It is a curved plane. I’m not sure if a special a uv map is required to make the texture follow the mesh shape.
In Zelda’s specific case it is probably a programmatic mesh, calculating vertices and uvs on the fly. Keep a history of the sword’s global positions and calculate the mesh using it.
Or you can do the effect “embeded” with the character’s animation. This is much cheaper, but (depending on the overall animation and movement) it can look obvious thay the trail and the character form a single block. As far as I remember SSB does it like this.