You're neither, you are the 'hirer'.
So, we may assume based upon your account that the Parking Charge Notices have been issued to you as hirer. In which case IF the creditor wants to be able to enforce against you as 'hirer' then the law, paragraphs 13 and 14 of Schedule 4 to the Protection of Freedoms Act applies:
So, were you supplied with the following in respect of each PCN?
a)a statement signed by or on behalf of the vehicle-hire firm to the effect that at the material time the vehicle was hired to a named person under a hire agreement;
(b)a copy of the hire agreement; and
(c)a copy of a statement of liability signed by the hirer under that hire agreement.and a copy of 'the notice to keeper;' initially issued to the lease company.
Yes, it's enough to make your eyes roll, but pl don't be tempted to ignore and want to get to grips with signs, lines, permits, tenancy agreements etc. All in good time.
For now, this is procedural.
https://www.legislation.gov.uk/ukpga/2012/9/schedule/4/enacted