Not going to provide a full detailed and step-by-step guide. Here are some ideas you might try:
- mod_rewrite rules
- extra webserver aliases: /usr/local/directadmin/custombuild/custom/webapps.list
- rename folders on disk literally: /var/www/html/ (directadmin hooks might help you to automate it)
- modify directadmin templates which save changes to /etc/httpd/conf/extra/httpd-alias.conf, /etc/nginx/webapps.conf, /etc/nginx/webapps.hostname.conf, /etc/nginx/webapps.ssl.conf
p.s. In order to complete the desired you will need to have certain knowledges and skills. In case you miss them, probably somebody else can provide a step-by-step guide.