You can't customize how the name looks specifically on the stream. It uses the formatname field with userlist reason so the Userlist Value Layout is what you'd use to alter it, but you'll need to ensure the profile URL part of it is properly mimiced in your custom HTML.
There are no plans to add such a feature to change name display on steam only. The entire point is consistency between plugins so using the formatname field through APIs accomplishes this very well. So for example if you want firstname with last initial you could use a Code field and use PHP to format it like that then substitute it into the formatname field layout usage. This gives you total control of how it looks everywhere on your site.
Regarding disabling the @ usages have added a feature ticket to look into implementing as would be a good addition.
forge.joomlapolis.com/issues/6140