USB device descriptors are contained within the USB devices themselves. For example the following code is taken from USB device code written using the Atmel Sofware Framework:
#define USB_DEVICE_VENDOR_ID USB_VID_ATMEL
#define USB_DEVICE_PRODUCT_ID USB_PID_ATMEL_ASF_CDC
#define USB_DEVICE_MAJOR_VERSION 1
#define USB_DEVICE_MINOR_VERSION 0
#define USB_DEVICE_MANUFACTURE_NAME "Peter Johnson"
#define USB_DEVICE_PRODUCT_NAME "IMP"
So I can easily change it by recompiling the program and writing it to the FLASH memory on the microcontroller because I have the source code. In your case however because the device has been developed by a third-party it leaves the following main possibilities I can think of:
The descriptor may be stored in ROM (read-only memory) or similar making it practically impossible to change. That's probably not that likely for a diagnostic type device.
The descriptor may be stored in FLASH or another style of non-volatile memory but might not have any form of bootloader, instead requiring attachment of a hardware programmer and depending on the device it may be hard to determine what's required.
It might have a bootloader allowing it to technically be changed, but the vendor might not be interested in assisting and/or providing the firmware binaries in an unencrypted form. Most production firmware is likely to have code protection enabled to prevent you reading it back.
The vendor might be very happy to assist and provide you with new firmware with the changes made for you.
The device may already have a documented / supported way to change the descriptor details.
The first thing I'd do is contact the vendor to ask them - if you're purchasing their hardware they might not be opposed to it being re-badged in some way. Failing that the next thing to do after you receive the device is to pop it open and see what sort of chip is used for the USB interface and doing a search for further details on the part number.
For a diagnostic tool which is presumably a relatively low-volume product it's likely to either be a microcontroller or some sort of USB bridge chip like a USB to serial converter. Some manufacturers like to remove part numbers to obfuscate their designs and the datasheets for some chips are only available under NDA, but there's not really any way to know until you receive the device.