While the prompt for the new keyring and password is still sitting in the terminal, check what processes are connecting to the terminals on the system:
user@pc:~$ ps axo stat,tty,pid,pcpu,comm
STAT TT PID %CPU COMMAND
Ss ? 1 0.0 init
S ? 2 0.0 kthreadd
S ? 3 0.0 ksoftirqd/0
Ss+ tty1 1297 0.0 getty
Ss ? 1638 0.0 screen
Ss+ pts/2 1639 0.0 bash
Ss pts/3 1640 0.0 bash
S ? 3559 0.0 check-new-relea
Ss pts/1 4952 0.0 bash
Where "man ps" will explain the various possible outputs (the example above uses BSD format)... and the huge selection of possible filters.
stat STAT multi-character process state. See section PROCESS STATE CODES for the different values meaning.
tty TT controlling tty (terminal). (alias tname, tt).
pid PID a number representing the process ID (alias tgid).
pcpu %CPU see %cpu. (alias %cpu).
comm COMMAND command name (only the executable name).
Look for processes that are running in a terminal like tty or pts, and look for things like gnupg, agent, and others linked to the desktop that you have running (like kde wallet manager):
user@pc:~> ps axo stat,tty,pid,pcpu,comm | grep agent
Ss ? 2991 0.0 ssh-agent
Ss ? 2992 0.0 gpg-agent
The prompt may well be from a wallet manager that is trying to store the password for your WiFi connection, for example, but is not able to locate an existing default wallet.
If you don't know what the terminal ID is, then kill the suspect process, and it should disappear, confirming that you got the culprit. Obviously, killing processes could make your system unstable, so reboot after you ID the process, if you guessed incorrectly. A brute-force approach.
Note that each time you login, subsequently, you will be prompted for the wallet password, so that the system can then access the stored passwords.
In the Gnome desktop system, taken from GNOME/Keyring, you need to have a default wallet or else passwords are not remembered:
If you get a password prompt every time you login, and you find that
passwords are not saved, you might need to create/set a default
Ensure that the seahorse package is installed, open it ("Passwords and
Keys" in system settings) and select View > By Keyring. If there is no
keyring in the left column (it will be marked with a lock icon), go to
File > New > Password Keyring and give it a name. You will be asked to
enter a password. If you do not give the keyring a password it will be
unlocked automatically, even when using autologin, but passwords will
not be stored securely. Finally, right-click on the keyring you just
created and select "Set as default".