Many Linux distros (typically Debian and derivatives) have a
/dev/serial/by-id directory. This shows the full "hardware" name of the serial USB device. Watch this directory while plugging and unplugging to identify your device.
Create a symbolic link between that full name and some short convenient name in the user's home directory. That full path (/home/me/myserial) is the "com port" to use in programs. This is stable across plug/unplug/reboot because of the symlink.
my@host:~$ ls -lA /dev/serial/by-id
lrwxrwxrwx 1 root root 13 Jun 11 07:21 usb-FTDI_FT232R_USB_UART_ANZ1SMDF-if00-port0 -> ../../ttyUSB2
my@host:~$ ln -s /dev/serial/by-id/usb-FTDI_FT232R_USB_UART_ANZ1SMDF-if00-port0 /home/me/myserial
This creates a symbolic link :
/home/me/myserial that points to the USB/Serial converter whenever it is plugged into the host.