What bootloader does the Arduino Micro come with?
Try looking at https://github.com/arduino/Arduino/blob/master/hardware/arduino/avr/bootloaders/caterina/Descriptors.c

Inside that is:

/** Device descriptor structure. This descriptor, located in SRAM memory, describes the overall
 *  device characteristics, including the supported USB version, control endpoint size and the
 *  number of device configurations. The descriptor is read out by the USB host when the enumeration
 *  process begins.
 */
const USB_Descriptor_Device_t DeviceDescriptor =
{
    .Header                 = {.Size = sizeof(USB_Descriptor_Device_t), .Type = DTYPE_Device},

    .USBSpecification       = VERSION_BCD(01.10),
    .Class                  = CDC_CSCP_CDCClass,
    .SubClass               = CDC_CSCP_NoSpecificSubclass,
    .Protocol               = CDC_CSCP_NoSpecificProtocol,

    .Endpoint0Size          = FIXED_CONTROL_ENDPOINT_SIZE,

    .VendorID               = DEVICE_VID,
    .ProductID              = DEVICE_PID,
    .ReleaseNumber          = VERSION_BCD(00.01),

    .ManufacturerStrIndex   = 0x02,
    .ProductStrIndex        = 0x01,
    .SerialNumStrIndex      = NO_DESCRIPTOR,

    .NumberOfConfigurations = FIXED_NUM_CONFIGURATIONS
};


...

/** Product descriptor string. This is a Unicode string containing the product's details in human readable form,
 *  and is read out upon request by the host when the appropriate string ID is requested, listed in the Device
 *  Descriptor.
 */
const USB_Descriptor_String_t ProductString =
{
    .Header                 = {.Size = USB_STRING_LEN(16), .Type = DTYPE_String},

    #if DEVICE_PID == 0x0036
    .UnicodeString          = L"Arduino Leonardo" 
    #elif DEVICE_PID == 0x0037
    .UnicodeString          = L"Arduino Micro   "
    #elif DEVICE_PID == 0x003C
    .UnicodeString          = L"Arduino Esplora "
    #else
    .UnicodeString          = L"USB IO board    "
    #endif
};



  and how would I go about building and uploading a modified bootloader?


You would run the Makefile which is in the same directory as the above file. Then send the resulting .hex file to your device.