UPDATE:
By now with the code below, I do get a list of the letters in the alphabet, and when clicking on one of those, the place names starting with that letter do appear, and are correctly clickable. But I still get the error about the Column aliases when I click on 'show counts'...

class PlaceFilter(admin.SimpleListFilter):
    title = 'first letter of place name'
    parameter_name = 'letter'

    def lookups(self, request, model_admin):
        qs = model_admin.get_queryset(request)
        letters = list(string.ascii_uppercase)
        options = [(letter, letter) for letter in letters]
        if val := self.value():
            print(val)
            if len(val) == 1:
                sub_options = list(qs.values_list('place__name', 'place__name').distinct() \
                            .filter(place__name__iregex=rf"^('s-|'s )?{val}") \
                            .order_by('place__name'))
                val_index = options.index((val, val))

                index = val_index + 1
                for option in sub_options:
                    options.insert(index, option)
                    index += 1
                        
        return list(options)
    
    def queryset(self, request, queryset):
        if self.value() and len(self.value()) > 1:
            return queryset.filter(place__name=self.value())