Yep. The SSID is a broadcast and assumed to be publicly available. If this bothers you, one solution is to hide among the multitudes and name your SSID as DEFAULT, LINKSYS, BELKIN, or a variety of other common names. The problem here is that what Google and similar snoopy companies really want is your wireless routers MAC address, so that it can distinguish between the multitude of nearly identical SSID's. While MAC addresses are assumed to be unique, there are plenty of counterfeits and contrived MAC addresses. However, the combination of MAC address and SSID is probably unique.
Turn off your wireless access point when you're not using it. Hiding the SSID does nothing useful as it can extracted from the management packets. However, if you're really really really paranoid, I recommend an expect web script, that logs into your wireless router, changes the SSID at regular intervals. Here's a starting list: This should thoroughly confuse Google. Unfortunately, it will also confuse users of your Wi-Fi router, but sacrifices must be made in the pursuit of anonymity. Except for one batch of cheap wi-fi access points I once bought that all had the same MAC address. This was long ago, and they have surely been recycled by now.  My home SSID is my home address. My office was the office address, but one of the other businesses in the building decided to use the same SSID, so I changed it to something obscure. Most of my customers have either the owner name, company name, or address as the SSID. If there's a problem I want them to be found.