Security risk, what security risk
First you want know whether or not other people can see your computer, if they can, there will be no intruder alert coming from your system to tell you you are being watched..
--open wireless is a good example of this, almost anyone can spoof or monitor a users computer and obtaining their account details and passwords when they login to social networks, and possibly change or takeover their user profiles..That's a security risk..
Having your computer name appear on someones browser/file manager isn't
The way you find computers/devices is via pings to an IP address range, or you can simply use a wireless or network monitor application if it makes it easier..
--web sites sometimes ignore pings (ICMP), but most home users don't
Both what is returned (the devices echo, a ping) and what isn't (the device gap tells the monitor where the device is or might be!
If you are concerned about security, you might consider a security intrusion detection tool, a rootkit checker, and looking at your system logs every so often + a firewall (IPTABLES), it is started automatically in Ubuntu/mint (ufw)http://sectools.org/tag/ids/