If the host name is public, it doesn't work.
If the host name is not public and internal DNS only points to internal IP, the Synology is not going to respond to it from externally, because it's external DNS-ing doesn't know it.
Not sure which "next, "next" menus you're talking about there.
For them to traverse public to private, they would need to be logged into device using either NAS UI or ssh - in which case I have bigger issues.
Risk, I'm willing to accept.