Does it matter that my passport and travel insurance have different names on them
There is no legal requirement for travel insurance and passport details to match. In the event of a claim we will need to establish that the person making the claim is the person insured with us, but the passport is not essential to that process.
In any event, you should be aware that this is a company insurance and not your personal one. The official documents for proving insurance are those held by your employer and made available to you through the company intranet which do not carry named individuals anyway. All authorities who might require such evidence are well aware of the nature of such corporate policies and will accept these. Please do NOT use the unofficial versions we send for information purposes only, for official purposes.