You can call the process whatever you wish in monit configuration files - it doesn't need to match the executable. So:
check process searchd_app1 with pidfile /var/www/app1/shared/pids/production.sphinx.pid
start program=....
stop program=....
check process searchd_app2 with pidfile /var/www/app2/shared/pids/production.sphinx.pid
start program=...
stop program=...