e.g.
current service name: postgresql.service
desired service name: postgresql-9.1.service
Run following commands to change service name;
Step 1: Stop current service
# systemctl stop postgresql.service
# systemctl daemon-reload
Step 2: Change service name
# cd /usr/lib/systemd/system
# mv postgresql.service postgresql-9.1.service
Step 3: Start and enable new service
# systemctl start postgresql-9.1.service
# systemctl enable postgresql-9.1.service
Step 4: Check service status:
# systemctl status postgresql-9.1.service
Step 5: Make sure that service runs properly
# journalctl -u postgresql-9.1.service