The whole point of programming to an interface is that you should be able to substitute one implementation with another implementation without changing the correctness of the system. This is also known as the Liskov Substitution Principle.
Thus, if you were to rename your interfaces based on a concrete implementation, it would be a Leaky Abstraction.
So, you shouldn't rename your interfaces for that reason. As Robert C. Martin explains in Agile Principles, Patterns, and Practices, "clients […] own the abstract interfaces" (chapter 11). Thus, you should name the interface based on how the client perceives it, not how it's implemented.