Use systemd to restart puma after reboot. Put this file at /etc/systemd/system/puma.service. Please check those paths in ExecStart and ExecStop carefully.

puma.service of rbenv

[Unit]
Description=Puma Rails Server
After=network.target

[Service]
Type=simple
User=deploy
WorkingDirectory=/home/deploy/apps/AppName/current
ExecStart=/home/deploy/.rbenv/bin/rbenv exec bundle exec puma -C /home/deploy/apps/AppName/shared/puma.rb
ExecStop=/home/deploy/.rbenv/bin/rbenv exec bundle exec pumactl -S /home/deploy/apps/AppName/shared/tmp/pids/puma.state stop
TimeoutSec=15
Restart=always

[Install]
WantedBy=multi-user.target

//////////////////


[Unit]
Description=Puma Rails Server
After=network.target

[Service]
Type=simple
User=root
Group=root
WorkingDirectory=/home/deploy/railsapp/current
ExecStart=/home/deploy/.rbenv/shims/bundle exec bundle exec puma -C /home/deploy/railsapp/shared/puma.rb
ExecStop=/home/deploy/.rbenv/shims/bundle exec bundle exec puma -S /home/deploy/railsapp/shared/puma.rb
PIDFile=/home/deploy/railsapp/current/tmp/pids/puma.pid
TimeoutSec=15
Restart=always

[Install]
WantedBy=multi-user.target

puma.service of RVM

[Unit]
Description=Puma HTTP Server
After=network.target

[Service]
Type=simple
User=deploy
WorkingDirectory=/home/deploy/apps/shiftweb/current
Environment=RAILS_ENV=production
ExecStart=/home/deploy/.rvm/bin/rvm ruby-2.6.5 do bundle exec puma -C /home/deploy/apps/shiftweb/shared/puma.rb
ExecStop=/home/deploy/.rvm/bin/rvm ruby-2.6.5 do bundle exec pumactl -S /home/deploy/apps/shiftweb/shared/tmp/pids/puma.state -F /home/deploy/apps/shiftweb/shared/puma.rb stop
Restart=always
KillMode=process

[Install]
WantedBy=multi-user.target