You're right - the data is stored as the 'name' in the database. The 'name' / 'label' pair in your Survey123 choice list is converted into a coded domain when you publish to ArgGIS Online which is then used when viewing your data through the website.
You can prove this to yourself by opening the Service URL of your layer and then Query the REST service:
My example is using:
and the Query result is:
Hope this helps,