The first question is NDA. In my current company, I'm only allowed to list about half of the clients I've worked with from a legal perspective. Next, you should make sure that your company handbook does not directly or indirectly prohibit you from posting to LinkedIn about your work with the client – it may be against your own firms rules.
When it comes to my résumé as well as LinkedIn, I generally put the name of the company I work for, and then include the client in the description of one or more of the tasks I worked on. So, for example:
Parse3 Communications (2012)
- Created the Nair product selection tool for Church and Dwight
The reason I generally prefer this format is because while I did do work for Church and Dwight, I did not answer up their hierarchy and my performance was not evaluated by their company.
You also don't want anything on LinkedIn which can be considered misleading. An HR person might ask questions, or might have even formerly worked at the company. Saying, "well, technically I didn't work for them" does not come across well.