It’s not super-specific, but your IP Address and location do get recorded.
So, let’s say you live in Queens, and your crush’s name is “Sally Draper.” If Sally has an analytics tracker, she can see that someone who lives in Queens used the search term “Sally Draper,” to find her site, and that the person spent 10 minutes clicking through. Not a huge deal, but while Sally probably gets a lot of direct hits to her site, it’s different knowing that someone is actually googling her. And depending on how many people Sally knows in Queens, she may be able to infer exactly who is doing the googling.
Of course, it’s hard to know who has a site tracker and who doesn’t, but if you’re paranoid, you can always avoid the issue by simply opening a new window and typing the website’s URL (www.sallydraper.com) directly into the address bar, instead of clicking from the Google results, which tracks the search term. There are also ways to hide your IP address entirely.
Okay! Stalk away!