Your CDN or you could initiate the revocation. The CDN can request the revocation most likely through the account they have with the CA and from being the "owner" of that specific order.
You can request a revocation still, even though you are not the owner or purchaser of that specific certificate. The CA will request you to prove you are the owner of that domain. If you can prove to the CA that youre the owner of the domain, they will revoke the certificate.
You ultimately are the party granting or denying the use of a certificate for your domain. You can authorize another party to buy certificates on your behalf. And you can revoke that authorization at any time as well.
Each CA has a their own revocation policies and its worth checking out those documents. But the CA/B forum which sets rules and standards for CA's, does state who is allowed to request a revocation. See section 4.9 of the Baseline requirements.
4.9.2. Who Can Request Revocation
The Subscriber, RA, or Issuing CA can initiate revocation. Additionally, Subscribers, Relying Parties,
Application Software Suppliers, and other third parties may submit Certificate Problem Reports informing the
issuing CA of reasonable cause to revoke the certificate.
CA's are allowed to process requests from "relying parties" who can provide reasonable evidence that the certificate should be revoked. In the scenario presented in the OP, you would be the relying party and your CDN would be the subscriber.
Relying parties are defined as:
Any natural person or Legal Entity that relies on a Valid Certificate. An Application Software
Supplier is not considered a Relying Party when software distributed by such Supplier merely displays
information relating to a Certificate.