You are right ! If you change the name of a property across one or more documents, it will be treated as a new field. By applying this rename to every document in the collection, all the data will transfer to this newly named field, leaving the original field with NULL values in its place.
To better understand the situation, you can read more here : https://learn.microsoft.com/en-us/azure/cosmos-db/analytical-store-introduction
Based on this thread :
If you rename a property, in one or many documents, it will be considered a new column. If you execute the same rename in all documents in the collection, all data will be migrated to the new column and the old column will be represented with NULL values