What is the name of the device that connects two computers by means of a telephone line?

You've answered your own question. The device is called a Modem (Modulator demodulator).

Some computers needed a separate device, later ones had the modem built in and only needed a telephone cord, between the computer and the phone socket.

These days broadband is used. The computer's Local Area Network (LAN) socket is connected through a device called an ADSL (Asynchros Digital Subscriber Line) Router.

This needs to connect through a filter to the telephone line, to stop interference on the telephone, which can be used at the same time.