When you do this assignment:
name = null
name is smart casted to Nothing?, which is problematic. Nothing is the subtype of every type, and so you become able to call any accessible extension functions of any type, according to the overload resolution rules here.
Compare:
fun main() {
var name: String? = "Denis"
name = null
print(name?.myExtension()) // works
val nothing: Nothing? = null
print(nothing?.myExtension()) // also works
}
fun Int.myExtension(): Nothing = TODO()
Note that allowing you to call any extension function on Nothing is perfectly safe - name is null anyway, so nothing is actually called.
Char.toLowerCase and String.toLowerCase happen to be two of the extension functions that are accessible, and you can call both on name, which is now a Nothing?. Therefore, the call is ambiguous.
Note that smart casts only happens in assignments, not in initialisers like var name: String? = null. Therefore, name is not smart casted to Nothing? in this case:
fun main() {
var name: String? = null
print(name?.toLowerCase()) // better to use lowercase(), toLowerCase is deprecated!
}
For the reason why, see my answer here.