An SEO or marketing agency that sets up search engine accounts under the their name; 1) is taking the lazy path. Its easier to do it that way or, 2) they intend to keep all the work they do (with your money). When you stop paying, you don’t own anything. The good news is that Google has some guidelines you should know about concerning the Client-Agency relationship.

https://support.google.com/business/answer/3038177?hl=en&ref_topic=4540086

Authorized representatives must:

  • Never claim a business listing without express consent from the business owner.
  • Never make false, misleading, or unrealistic claims.
  • Never use harassing, abusive, or untrustworthy tactics with potential or existing customers.
  • Always work directly with the business owner to complete verification.
  • Always ensure that the business owner understands what Google My Business is and where Google My Business data is used.
  • Always keep the business owner informed about which actions the authorized representative will take on the business listing.
  • Always follow Guidelines for representing your business on Google. Note that the phone number and website for a listing should always be the single, authoritative phone number and website for the business and be verifiable by the business owner. Website content must be owned and managed by the business owner.
  • Always respond to management access requests promptly, and always transfer listing ownership to the business owner immediately upon request. Authorized representatives must, whenever possible, encourage the business owner to create an account, own the listing, and add authorized representatives as managers.

Failure to adhere to these policies may result in a suspension for the listing and/or account.