Again, it depends on the specific name itself.
I presume that the MyBook/MyBooks are just examples and not the exact names you have in mind.
For example, in English some words are the same in both plural and singular, such as "fish." Yes, some people say fishes, but it's not standard; therefore, Myfish would be far superior than myfishes.
Now if the name is MyCar/MyCars, I would choose MyCars over MyCar, no matter what Estibot says (which is just a bot) because I would intend to sell many cars, not just one.
MyCar.com would be a domainer's domain, a trophy domain, but if I intended to do business, I would select MyCars over MyCar -- every day of the week.
If I were to set up up a forum about cars, then I would choose MyCar because individuals would be discussing their individual cars, and it's a clean kicky name for that purpose.
So what I'm saying: we can't give you a definitive opinion based on a sample -- there are too many unknown variables having to do with the term itself and intended usage.
Obviously, you can't really reveal the actual domain on a forum (please don't), so you need to do a little checking on your own and not take general advice offered on a forum too seriously.
Food for thought.