Unfortunately, this is not what the standard says. The ISO 45001:2018 standard does not specifically require that roles, responsibilities and authorities be assigned by name, only that they need to be assigned for the OHSMS. In fact, it is often helpful to use a more flexible term in your documents rather than the name or position title as when people change positions in your organization, titles change, or people leave you will then need to update all of the documents to reflect these changes. That being said, it is a helpful best practice to know who authored a document for the purposes of clarification when questions arise.
For more on OH&S responsibilities, see this article (the information has not changed with the release of ISO 45001): How roles and responsibilities have changed in DIS/ISO 45001, https://advisera.com/18001academy/blog/2016/04/06/how-roles-and-responsibilities-have-changed-in-disiso-45001/