Hello @LundEmma
Firstly, if the URL to your Jira instance is not in the format of ‘(companyname).atlassian.net’ then you’re using Jira SERVER or Jira DATA CENTER, not Jira CLOUD, so you’ve used the wrong subject tag for your question.
For those versions of Jira, you do indeed use the issue-assign endpoint and set the accountId to null to allocate no assignee, just as it says in the documentation.
Since you haven’t provided any code samples of your API request, there’s no way to know whether or not you have created a valid, properly formatted request.
Next, you said you got a 405 error in response. That normally indicates that you tried to to a POST request to the endpoint, not a PUT request.
Also, can you remove the assignee from the Issue via the web GUI to confirm the Project hasn’t been configured to add a default assignee to every Issue, so having an Issue with no Assignee would not be possible?