Use an F expression:
from django.db.models import F
either in update():
Counter.objects.get_or_create(name=name)
Counter.objects.filter(name=name).update(count=F("count") + 1)
or on the object instance:
counter, _ = Counter.objects.get_or_create(name=name)
counter.count = F("count") + 1
counter.save(update_fields=["count"])
Remember to specify update_fields, or you might encounter race conditions on other fields of the model.
A note on the race condition avoided by using F expressions has been added to the official documentation.