You are switching from one normal user (you) to another normal user, say joe, right?
The following is your shell prompt, defined in the environment variable PS1:
user@user directory $
After switching to joe, you see joe's shell prompt. And he did not configure to show anything fancy in the prompt, so only the default prompt is shown, which looks just like:
The second one is the default of the plain shell program, yours is probably the default of the linux distribution.
Try setting PS1 to the same it is in your account, it should help:
user@usersBox directory $ echo "$PS1"
joe@usersBox directory $
Replave the ...... with the value shown by the
The word after the "@" is normally the name of the computer, so I guess you gave the computer the same name as your user name during setup.
To make it less confusing in the example, I changed the computer name to "usersBox".
Maybe he removed the variant you have intentionally. But as likely, it's caused by some random minor technical issue, and he would be ok if you change it for him too, in his startup files, like ~/.bashrc or similar, depending on the kind of shell used by him.