What does Ootsutsuki mean?

[Lady Mokusei]

The on readings (the individual meanings of each character) are irrelevant. It sometimes helps if the kanji have some sort of relation to the word they're spelling (for memorization sake), but in this case, I think that it's just a name. Trees 木 and forests 森 in Japanese surnames are very common.

For example the word for "prey" includes a character for eclipse 食, which has very little relation to the word it's used to spell. Just like how we don't look at the individual letters but the whole word when we are reading English (we don't go "There's a 'b' and then an 'a' and then a 't' ... oh yeah, that makes 'bat'"), people who read kanji are able to read words even if they don't always know the meaning of all the kanji that make the word.

Since the kanji in the name appear to be meaningless, but people may still be eager to find out if the name has any significance, another thing that people might try is to see if Kishimoto borrowed the name from a historical or a fictional/mythological figure and find out if there is a connection between the two.

:erm: First of all, remember that we are talking about the word which denotes the name of the family. Then you probably already know (It looks like you learn Japanese as well.) a lot about XX century reformations, therefore about our subject. Also, pay attention that we are speaking about language used in manga.
These are literal translations of each kanji which denote a word, that's right. When we are talking about surnames, theoretically, you can translate every of them. Why? Because kanji are not individual letters...kanji are single words made of bushu, smallest units which don't have any real meaning (that would be letters in the alphabet if we'd start comparing two languages).