The “designation” of this Supercharger in the Tesla nav is whatever Tesla decides to call it. That is what we are talking about here.The designation of the site isn’t Thousand Oaks East. It’s just Thousand Oaks — the the section of Thousand Oaks Blvd. east of Moorpark Rd. is E. Thousand Oaks Blvd. West of that (and entering the Oaks Mall), it’s W. Thousand Oaks Blvd.
The Supercharger name in this TMC thread title is set to be whatever Tesla decides to call it to avoid confusion.
You of course are welcome to call this Supercharger by whatever name you choose. But if your name doesn’t match Tesla’s name, whoever you are trying to communicate with may not understand which Supercharger you are referring to.
If you think Tesla has misnamed this Supercharger, I suggest you contact them and try to change their minds.