The rule of thumb is that the number of times you change your strings per season should equal the average number of times that you play tennis per week. So if you play tennis twice a week, then you should change your strings twice per season.
Of course, this rule of thumb becomes irrelevant if you hit the ball hard enough to break strings regularly. In this case, you can forget about the rule of thumb and replace your strings when they break.
Personally, I prefer to use Wilson Super Spin tennis string. It’s a hexagonal shaped string with edges that bite into the ball and create extra spin. Unfortunately, these edges also bite into each other. So I break strings more often than most players.
The faded logo — getting back to Geoff’s question — is completely irrelevant. Most pre-strung racquets will come with the manufacturer’s logo stamped onto the strings. At some point, however, the owner will need to replace the strings; the new strings will not have the logo stamped on them.
The exceptions to this are pro tennis players like Roger Federer or Serena Williams who have endorsement contracts with racquet manufacturers. Every time their racquets are restrung, a new logo is printed on their strings.
At the other end of the spectrum are recreational tennis players who just go out and bump the ball around every now and then. These players will rarely, if ever, have to replace the strings on their tennis racquets.