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to have the search name reflected in the queries please do the following steps:
1. Create a search and save the search
2. Execute it and open the query menu
3. Add to an assortment
That being said, it does not mean that all futer updates of the search will update the assortment. It is just a hint which assortment was used initially.
To update it you still need to remove this condition (not the whole assortment!) again, and re-add it with steps 2 & 3.