[MKairys]

Lumia Icon with Denim, tablet with Windows 8.1. The broadcast name in my Internet sharing settings always shows up in the tablet's available networks list. I would prefer it not! (Forget this network doesn't help either).

[Harrie-S]

Lumia Icon with Denim, tablet with Windows 8.1. The broadcast name in my Internet sharing settings always shows up in the tablet's available networks list. I would prefer it not! (Forget this network doesn't help either).

This is a feature. If you switch on the bluetooth the phone automatically broadcasts the name and you can connect to it on your tablet, without enable the internet sharing on your phone.
Not sure if switching off bluetooth is an option for you. But that is the only way i know to prevent the broadcasting..

[sugarbowl06]

I have noticed this too. Make sure you have a strong password set.