Go to the DVLA check MOT status website which should show the personalised registration and the fact that the vehicle is covered by an MOT, see example below.
Take a screenshot of the DVLA website and upload the screenshot as evidence that the vehicle is covered by an MOT.
The insurance certificate you hold should certainly quote the personalised registration, unless the vehicle is covered by fleet insurance.
Please note that the DVLA website only confirms that a vehicle is taxed and has an MOT, not that the vehicle is insured.