Who should own the customer data? Customer success or Revops or Sales or another department?

The answer is, it depends. It depends on exactly what you're referring to when you say "customer data," how your org is setup, and where the data lives. 

Customer data is many things:

• Firmographic/demographic information
• Contract, pricing, billing information
• Product usage
• Communication (ex. emails, meetings, calls)
• Rep-created (ex. account plans, notes)

There needs to be an owner for each of these pieces and an owner on the strategy of how to connect them all into a single view. The latter is often a massive project that needs executive-level buyin and resourcing. If it's treated as a side project that one team can own, it won't be complete. 

I'd focus on the business case and generating buyin for the initiative and then come up with owners for the subsets of the data. (ex. firmographic/demographic information would likely be owned by RevOps, sales might be responsible for Contract information, product for product usage, etc.). Select the owner for the overall project and continued maintenance based on the data infrastructure. This is likely corp eng, product, or an overall bizops/program mgmt team.