When Doom starts, under doom-editor.el it checks for the environment variable $EMACS_SERVER_NAME to set the name of the server allowing you to connect to different instances by name.
Before you launch Doom, you can set $EMACS_SERVER_NAME to a name of your choice.
Then, emacsclient can be told to use that server name by setting the environment variable $EMACS_SOCKET_NAME prior, or by using its command line argument -s and providing the name.
Depending on your use of emacsclient, like running Doom’s provided org-capture script, without editing that script to add the arguments, it may be better to use the environment variable method. Otherwise, you’ll have to develop your own scripts/methods of managing these considerations.
Additionally, emacsclient supports the alternate editor (-a) argument which if left blank launches the default (Emacs) configuration in daemon mode if one isn’t already started. Or, you can have it run an instance of Doom (doom run) in your alternate location which would also accomplish the same. Just some food for thought, good luck.
P.S. I’ve tested the above and it does work as expected. You’ll just have to configure it for your use.