See https://wiki.openstreetmap.org/wiki/Key:destination

`destination=*` should go on the road you turn into, not the road you turn from, but it only really works when there it's not different from each of the from roads, and even then it's usually for a place not a street (see https://wiki.openstreetmap.org/wiki/Key:destination:street for that). On the first wiki page you can also see there is destination:lanes which can be set per-lane on the from way.

However there is yet another method (first was destination on the to way, second was destination:lanes on the from way) which is use a relation, which exists here at https://www.openstreetmap.org/relation/10699075/history this can capture more detail about the destination sign.