A Arduino Pro Mini doesn’t have a on-board USB connection at all. It’s ATMega328P based. You usually connect an external USB-to-serial adapter onto its serial pins to be able to program it.
Other boards like ATMega32U4 based ones (Arduino Pro Micro) are native USB and can present a different “USB Manufacturer” and “USB Product” string to the computer.
PlatformIO has no capability to rename a COM port or label a COM port. If you really want that, you need to modify your Winodws registry to get a new “Friendly Name” for your COM port. “COM5” will likely always though, that is the designation of the COM port of the Windows operating system. See https://superuser.com/a/1821751. I would not recommend doing that modification.. because why? Just for aesthetics? Also, that change would only work on your local computer, not on any other computer. The USB-to-Serial adapter will always send its hardcoded USB manufacturer and product string.
An easier way would be by USB VID and PID (vendor and product ID). They’re predictable for the various versions of the Pro Micro.
You can arbitrarily change the VID, PID, manufacturer (vendor) and product strings in PlatformIO with an extra script as e.g. outlined in
A good serial / USB library should give you access to these attributes. Try actually reading out the manufacturer or product string, or at least PID and VID.