We always assign the API key to the Upwork account of the person who submits the request.
If you are a company or an agency and you don’t feel comfortable giving your real API credentials to your developers, one option is to create two API keys - one for development purposes (to share with your developer), and another for production (that you don’t share).
If you’re a developer working for a client who would like to use the API, you should discuss with your client who will own the key. Normally, the owner of the app keeps the key/secret for the application, and that key should be requested/created by the owner. You can create your own for development purposes.
Keys are tied to the requesting account and Upwork can’t transfer ownership of the API. If the person who had that account leaves your company, in most cases you’ll want to request a new API key and stop using their old one.