Unfortunately this is not an easy thing to do. Default membership popup, which I assume you are using in your theme is built with React.. It generates a portal.min.js which is then included in the site. It has a few switches for the admin to change, as you can see on Admin->Settings->Members->Portal page (like Display name in signup form toggle). It does this by making an API call (‘members/api/site/’) to the server, getting site details and using that data to render React components. So unless there are more switches and inputs added to this functionality by Ghost team, you have a few options
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Do not use the default membership portal (signup/signin popup,etc.). You’d need to have someone create similar functionality with HTML/CSS/JS in your theme
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Clone GitHub repo, modify, build it and somehow replace the loaded default portal.min.js(which may be hard itself. There is a discussion about it here ). As an example,you can check Sign up page
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This is a bit of a hack with Code injection and the least reliable way, but it seems to work. I did a quick and dirty one here which you can understand how it can be done. I had to add in timeouts to give React time to load and render components. Add this to your pages using Code Injection