How/where can I change the book title?

How or where can I change the title of my manuscript/book? Should I “save as” the new name, and start a new file/project or is there a more simpler and more direct way?

(Please read through before doing any of those operations.)

The book title is usually the name you gave your project.
First place to look is here (Compile panel - Windows version screenshot):
Inked2022-03-29 16_05_43-Window_LI

1- In the case nothing is to be found there (which would imply previous user manipulation - if I am not mistaken),
try renaming your draft folder.

2- If that still doesn’t do :
In the compile format (from the list on the left side of the compile panel),
locate <$projecttitle> and replace it with <$draftname> and rename your draft folder accordingly.

3- You could also manually replace <$projecttitle> with your desired title. (But I don’t advise it, as it will impact other projects using the same compile format.)

Otherwise, if you are not accustomed to placeholders, using “save as”, just as you said, is probably, and by far, your simplest option.

→ You could also just rename the project directly on disk while it is closed. I don’t think that would be a problem. (But I would do a backup first, just in case.)
→ It works fine under Windows, but I can’t say for a Mac.

Yeah, you can safely rename the project name on the disk, and in most cases I would say that is preferable as Save As would leave behind an old copy with the previous name and potentially get confusing.

On a modern Mac (post around 10.14) you don’t have to bother with closing the project, the system updates running software with the name change seamlessly, and Scrivener is programmed to detect that and adjust accordingly.

But just simply typing in the title you want into the compile pane is probably easiest unless you want the project name to match the exported document title. That may not always be the case.