ESP32 Providing Multiple Bluetooth Servers From One Module

I have a ESP32 being used as a BLE HID device. However, I also need a way to send a stream of status information to the device so it may alter LEDs and values on a display according to external simulation data using a serial connection.
I believe I could add a HC-05 or similar module to my design and simply have two Bluetooth devices. The HC-05 does not have BLE, but that is not important for the purposes of this question.

If possible, I would like to advertise two servers from a single ESP32 without additional hardware. It is essential both services run side by side, so disconnecting and reconnecting as described in many posts is not a viable solution in this use case.

The questions are:
1: Can this be done? (Similar to how USB HID can advertise multiple services on one connection.)
2: If so, can they appear with two different names to avoid confusion as to which service is which?