A device that connects lots of devices and remembers which ones are connected to the interface is known as

Router

Explanation:

A router is a device that connects your home network that includes devices like the computer and the TV to the internet. It works by sending data packets between the devices in the network or between a device and the internet and to make sure that the packets are sent to the right place, the router assigns an IP address to all the devices. According to this, a device that connects lots of devices and remembers which ones are connected to the interface is known as router.

Router is the answer to your question.