is there any reason (safety?) why someone should rename the ASP.NET Session Cookie Name or is it just a senseless option of ASP.NET?
With cookie prefixes, you can add a security attribute to your cookie by naming it a special way. So in that case renaming your ASP.NET session cookie does have an impact on security:
__Secure-…
cookies can only be written from secure (HTTPS) sites.__Host-…
cookies can only be written from the same, secure domain. So not from subdomains or insecure (HTTP) sites.