There's now a new set of rules for using SL related terms. Here's links to the Official Linden Blog entry and the website information. We've got 90 days to adapt.
Logos, including their green eye in the hand one, are no longer okay. They have a new inSL logo that we're welcome to use under certain conditions. The logo can't be shown on a page with anything that might not be considered PG. (Interestingly, the example they use involves skins, which we've been told are acceptable to show in their entirety for sale in a PG sim, although not to run around wearing without clothes.)
Bloggers, forum posters, and people chatting are (more or less) in the clear. We are expected to use the standardized terms now. The company is Linden Lab, not Linden Labs. LindeX, not Lindex or lindex. SLurl, not slurl. Second Life is always two words and both words are capitalized. You can also refer to it as SL. Not 2ndLife, sl, or secondlife.