This is a very common question. To clarify, sometimes one partner holds the mortgage commitment completely in their name but both partners would like to be covered under a Mortgage Life Insurance policy.
Essentially, there is no problem with taking out Joint Life Insurance to protect the loan even if only one partner is named on the mortgage.
Even if only partner holds the mortgage it is often the case that both partners contribute to the monthly repayments, or one partner makes the repayments and the other partner covers other monthly costs.
There would be a significant dent to family finances if one partner were to pass away so taking out life cover for both partners usually makes complete sense.
With a joint plan the policy would pay out a lump sum designed to repay the loan if either partner named on the plan were to pass away. Both partners do not usually need to be named on the mortgage.
Essentially, Mortgage Life Insurance is just a brand of life cover and is not usually tied to the actual mortgage.
For more information please see the page: Guide to Joint Mortgage Life Insurance.
Please note this only applies to Life Assurance. In the case of Mortgage Payment Protection Insurance (MPPI) it is usually the case that both partners need to be specifically named on the mortgage for a payout to be valid.