How to change GitLab pages project site to user site

I have a GitLab project, which is a fork of another project (a blog) called vuepress. I have enabled GitLab pages for this project, so now to view my GitLab pages site I can visit:

https://my-name.gitlab.io/vuepress/

Now ideally I would like this to be a user website, rather than a project website (distinction here), so that the URL to visit my site would be:

https://my-name.gitlab.io

I have tried renaming my project to my-name.gitlab.io, but this doesn’t work (by “doesn’t work” I mean when I visit https://my-name.gitlab.io I get a GitLab 404). What can I do short of starting again from scratch?