In a remote shell, how can I find out from which computer I logged into the remote machine?

ssh always sets the SSH_CONNECTION environment variable in the remote shell to a value containing the client's and server's host and port.

This also works from non-interactive shells and on machines which do not have utmp/systemd/whatever (e.g. on your router or camera).

ssh root@unq 'echo $SSH_CONNECTION'
192.168.38.152 35466 192.168.38.1 22

Then you can do a reverse host lookup on that address:

ssh [email protected] 'nslookup "${SSH_CONNECTION%% *}"'
...
Name:      192.168.38.152
Address 1: 192.168.38.152 bursku.und

You can use w, who or even last.

Also you can check sshd logs, journalctl -u sshd -n 100

On my Red Hat 7 machine, I run who am i or who am I or who -m.
The last column will show the machine name where I logged in from (in parenthesis). If I am on my local machine, the last column will show my console/display ID. On my machine it is (:0).

Caveat This only works on an interactive shell.
ssh ScottieH@RemoteServer who -m will give unexpected results.
On my Red Hat 7 machine, It spews an error.
YMMV