F5 Big-IP Trust Internal CA Chain certificates for Web Servers

Happy Friday to yoo too pcourtois​ 

irule is you friend in this case
check this https://my.f5.com/manage/s/article/K13452

when HTTP_REQUEST {
    set hostname [getfield [HTTP::host] ":" 1]
}
when SERVER_CONNECTED {
    switch -glob [string tolower $hostname] {
      "sitea.com" {
          SSL::profile serverssl-siteA
      }
      "siteb.com" {
          SSL::profile serverssl-siteB
      }
      default {
        #default serversssl profile to be selected if Host header value cannot be matched with predefined values
        SSL::profile serverssl
      }
    }
}