The existing testnet today is testnet 4 created only recently.

The testnet you knew before then is testnet3  which was created to replace testnet 2 once people traded testnet 2 for money.  Which was created to replace testnet 1 when people traded that for money.  Testnet 3 was made purposefully defective in a number of ways so it went a long time before anyone was foolish enough to pay much for it, but it just goes to show that if you make something fool proof nature will just create a bigger fool.

TN1 was the only one that existed when Satoshi was still potentially around.  So no, the thing you call testnet wouldn't be linked to Satoshi.