You should use the same database for UCP and MDW.
Actually, you can't use a different database. UCP is in fact a specialized collection set that uploads its data to a MDW database. The MDW database is unique for a SQL Server instance and Data Collector cannot upload different collection sets to different MDW databases.
The database name for UCP must be "sysutility_mdw" and cannot be changed, so if you decide to activate UCP, you will have to stick to that name. That's why I always advise naming the MDW database "sysutility_mdw", so you can activate UCP in the future. To be fair, very few people use it.