Is a "dynamically" named Midi device possible?

[LeSuedois]

Hello,
I try to get this working since a while, but each time I fail :-|
The goal is quite simple:
The code is made on a Raspberry pi pico (RP2040, earlephilhower core), just some custom midi USB controller.. but up to 16 (every one sending on a different channel) of them on one host system. All the same, only a 4 position DIP switch to select the channel.
The embedded side is working quite well but I am aware that multiple MIDI devices with the same name may provoke unexpected behaviour. Also I trie to program a MIDI to OSC Bridge in python (noob level) and I realize that having many ports with the same name is quite disturbing to me. I look at a list with all the same interface name.

So I tried something like this (this should compile even if I didn't checked it, needs Midi.h from Arduino library manager):

#include <Arduino.h>
#include <Adafruit_TinyUSB.h>
#include "MIDI.h"

#define DEBUG

Adafruit_USBD_MIDI usb_midi;
MIDI_CREATE_INSTANCE(Adafruit_USBD_MIDI, usb_midi, MIDI);

uint8_t ID[4] = {10, 11, 12, 13};

void getID()
{
  // ID not zero indexed!
  id |= !digitalRead(ID[3]) << 3;
  id |= !digitalRead(ID[2]) << 2;
  id |= !digitalRead(ID[1]) << 1;
  id |= !digitalRead(ID[0]);
  id += 1;
#ifdef DEBUG
  Serial.println();
  Serial.print("Interface ID :\t");
  Serial.println(id);
  Serial.println();
#endif
}

void setupIDpins()
{
  for (int i = 0; i <= 3; i++) {
    pinMode(ID[i], INPUT_PULLUP);
  }
  delay(100);
  getID();
}

void setup()
{
  setupIDpins();
  delay(100);
  char nam[16];
  // MIDI channels are not zero indexed 1-16, 
  // here I like to have more like "MIDI-INTERFACE 0-F" 
  // hex identifier to respect a 16byte long Product Descriptor
  sprintf(nam, "MIDI-INTERFACE %1X", id - 1);
  USBDevice.setProductDescriptor(nam);
  usb_midi.setStringDescriptor(nam);
#if defined(ARDUINO_ARCH_MBED) && defined(ARDUINO_ARCH_RP2040)
  // Manual begin() is required on core without built-in support for TinyUSB such as mbed rp2040
  TinyUSB_Device_Init(0);
#endif
#ifdef DEBUG
  Serial.println();
  Serial.print("ID : ");
  Serial.println(id);
  Serial.print("\n Midi Name :\t");
  for (int i = 0; i < sizeof(nam); i++)
  {
    Serial.print(nam[i]);
  }
  Serial.print("\n\t\t\t");
  Serial.println(sizeof(nam));
  Serial.println();
#endif
}

void loop()
{
    delay(10);
}

But this doesn't work, the MIDI device is now recognized as "pico".
Until now I used :
USBDevice.setProductDescriptor("MIDI-INTERFACE "); usb_midi.setStringDescriptor("TinyUSB MIDI");

And this works fine!

Thank you for any ideas,
Simon