Can Ethereum be used for white label transactions and services?

I apologize if this is an amateur question but I am, after all, an amateur when it comes to this.

Basically, if a company (like a financial trading firm) wanted to create/have a white labelled or private blockchain network to use for their own customers would they be able to use dapps on ethereum to allow the blockchain tech to operate somewhat centrally?

If a firm did want to try and white label blockchain to protect some user information from being available to everyone how would they go about it? Can it be piggy-backed by Ethereum, would you have to turn to another blockchain or would you have to create a new blockchain network from scratch?