Facebook says it owns rights to the name 'book'

I'm not saying they're right, though; I'm just saying they're not crazy.

But they exist for a very good reason, and I could see copyright and patents being tossed out in toto before trademarks went away. (And yes, I consider that to have negligible probability too.) You have a right to know with what entity you are dealing, and that's the problem trademarks solve. To that end, a trademark does not just cover the literal thing trademarked, it is explicitly defined in terms of things that may confuse a normal person, because that is the entire purpose. "Sort of like" is the entire point.

I think the idea that these people named their product with no intention of trying to ride Facebook's coattails completely implausible. They knew what they were doing. They may not have realized it's illegal, but this is simply the purpose of the law being fulfilled. (And the odds that they did know what they were doing and acted in bad faith anyhow are definitely nontrivial.) This is little different than trying to sell a Sorny TV.

It is simply not the case that any Internet squatter can decide "I'm going to own the word Bedsheet, because nobody's thought to trademark it yet!" and then go troll anyone who uses a bedding image in their name. You have to actually build a valuable brand first.

Also trademarks can be lost if not defended, unlike patents and copyright.

The dispute between teachbook and facebook likely revolves around being confusingly similar, and could also be in part because they need to actively defend the trademark in order for it to be valid.

In the US, one at a time - but there could be a class of names which are confusingly similar to that name.

They either need to argue that the similarity "is likely to cause confusion, or to cause mistake, or to deceive as to the affiliation, connection, or association of such person with another person, or as to the origin, sponsorship, or approval of his or her goods, services, or commercial activities by another person" or dilution by blurring an "association arising from the similarity between a mark or trade name and a famous mark that impairs the distinctiveness of the famous mark".

The second (trademark dilution) only applies to famous marks (like Facebook), but can be used when the mark is only diluted, and there is no likelihood of confusion. However, "the degree of inherent or acquired distinctiveness of the famous mark" is important - and the distinctiveness isn't just in one particular market. English words are unlikely to be considered to be particularly distinctive, and 'face books' existed on paper before Facebook used the term.

In this specific case, it's even less frivolous. The Illinois company set up a social networking site for teachers and called it Teachbook. Even they aren't arguing that there's no overlap; they're simply surprised Facebook would care. But of course they do; they are required to defend their trademark or risk someone else claiming that they've abandoned it.