How to disable welcome message after SSH login?

The welcome messages are generated by the files residing in /etc/update-motd.d/.

From man update-motd:

Executable scripts in /etc/update-motd.d/* are executed by pam_motd(8) as the root user at each login, and this information is concatenated in /var/run/motd.

So if you don't want the outputs of those scripts upon login via ssh just remove the execute flag on them:

sudo chmod -x /etc/update-motd.d/*

Now if you want to show something you want upon login, you have two options:

• Make a script, put it in /etc/update-motd.d/, make it executable, also make sure it outputs on STDOUT.

• ssh has a Banner option. You can put the text in a file and set it in the Banner option so that the content of the file is shown upon login via ssh. Note that this is applicable to only ssh.

  Banner /etc/foobar
  

  From man 5 sshd_config:

   Banner  The contents of the specified file are sent to the remote user
           before authentication is allowed.  If the argument is “none” then
           no banner is displayed.  This option is only available for
           protocol version 2.  By default, no banner is displayed.
  

Another way that does not require administrative rights is to place an empty file called

.hushlogin

into your $HOME directory (using for example touch ~/.hushlogin).

Source that provides further info including a possible downside of this approach.

You can also nuke pam_motd altogether:

sed -i '/^[^#]*\<pam_motd.so\>/s/^/#/' /etc/pam.d/sshd

PAM calls pam_motd depending on the settings in /etc/pam.d, and typically the entries are:

$ grep pam_motd /etc/pam.d -R
/etc/pam.d/login:session    optional   pam_motd.so  motd=/run/motd.dynamic noupdate
/etc/pam.d/login:session    optional   pam_motd.so
/etc/pam.d/sshd:session    optional     pam_motd.so  motd=/run/motd.dynamic noupdate
/etc/pam.d/sshd:session    optional     pam_motd.so # [1]

Just commenting out the pam_motd lines from these files will disable it.