Absolutely. Your cell phone can also broadcast your actual name, as well. For example, if you have an iphone, and during setup you named it "Daves iPhone", they will see that information as well. They can also do a search on your MAC address, and at the least know who made your phone (i.e. it's manufacturer, Apple for iphone/ipad etc).
If you were dumb enough to do this at work, yes, it can literally be traced back to your phone.