I found a solution that seems to work correctly:

1. In power query I created a Supplier Table with distinct supplier column.
2. an index column
3. a custom column "anonymisedSupplier" - " Supplier " & [INDEX] to create "Supplier X" for each Supplier (where X is an index no)
4. for each Supplier name (160 suppliers) I created a separate column where Supplier name remains the same and all other suppliers are changed to their equivalent from anonymisedSupplier.
5. Added my 160 new columns as a field parameter.
6. Last step: Added the parameter into Rows section in the matrix visual + the parameter field into a slicer.

If anyone has a similar project to complete, I'm happy to share more details if needed.