Does the insurance cover gifts given to me?

Yes but you must be the legal owner of the property. In the event of a claim for an item for which you became the legal owner through a gifting, you must still be able to provide proof of ownership such as a document from a high street or online retailer showing the date of purchase and either the IMEI number, serial number or unique device identifier of a brand new gadget and confirmation of the gifting. Provided you can, then your item will be covered.