I'm pretty sure it is illegal for Eir Retail Sales guys to access any info from Eir Wholesale systems, to stop them poaching.Don't Vodafone piggyback on Eir's cabling so presumably Eir knows who you're with.
Thank you MangoJoe - apparently if you stand outside my house and check for WiFi your phone will tell you that we have Vodafone. I do not understand the hows and wherefores of this but it has now been changed. And no, someone standing outside cannot use our WiFi - it is password protected.