Liable for rent
You must be liable for rent. If you are jointly liable for the rent with others (eg, you have each signed the tenancy agreement), the amount of HB you get is based on your share of the rent (although, less commonly, it may not be an equal share if that seems reasonable to the local authority).
If you are in a couple, it does not matter whose name is on the rent agreement; either of you can claim. So if you are a student who is eligible for HB, you can claim for both of you, or if you are not eligible for HB, your non-student partner can claim for both of you.
There are some circumstances in which a local authority has the discretion to treat you as liable for the rent even when you are not legally liable – eg, if you have taken over paying the rent from someone else.