If you say the aim of Ben, you can also say Ben's aim.
If you say the objective of the project (which is not a person but an object), do you say the project's objective or the projects objective?
The objective "belongs" to the project, so you would use 's to indicate ownership. You can say "the project's name" or "the project's staff".
You could certainly use the apostrophe-s possessive about a project, but it would be unusual. We don't tend to use this this form when a thing is the possessor (see this answer).
You could stick to the of-possessive form, but for project we can also make a compound noun, for example project objective, project name and project team.
Similarly, with hill, you can say the top of the hill or the hilltop, but hardly ever the hill's top;