Can the name of the Wi-Fi be seen on any bill concerning the iphone?

Ok so here's the thing. I went over to a friends house and connected my phone to their Wi-Fi. Now iUsually use my own Wi-Fi at home or outside Wi-Fi.&i'm not a bad person or anything( or a kid, i'm 19 years old, in college living with my parents), i just have really strict parents&i'm not allowed to go to other people's house. So when my parents go to pay the bill, will they be able to see the name of the new Wi-Fi that was used on my phone?

No, definitely not