LibTooltip is fine. Or LibTip. Or, you could just name it after me and I'll be happy. :)
LibTooltip was fine, until I discovered that Norganna and company have their own library of the same name (which is also using LibStub) for EnhTooltip. So anyone using an addon that has our LibTooltip with Auctioneer or Gatherer will see stuff break. So, rename is unfortunately needed.
I didn't say obscure (obscure would not be clever), and most of the names suggested so far are worse in that they give a false impression of what the library is about (MultiTip/InfiniTip suggests multiple tooltips open at once and not multiple columns, for example).
I randomly like LibQTip. It's funny and unique at the same time, and still says that it's related to (tool)tips. Perhaps not as descriptive as it could be though. Then again who wants LibThatDoesLotsOfToolTipStuffWithoutQuiteBeingAsBigAsTablet?
Sorry if this is mentioned elsewhere in the thread, but there are 20 pages which is a bit much to read though.
In the original Tablet thread, there was talk of an advanced plugin for the library that would add the more bloaty things like being able to click lines on the tooltip.
Is this still planned once the basic library is complete or was the idea scrapped?