There are cases when a client insists that you restrain from publishing anything you've worked on with them. Would you charge them more or you have another policy?
The Apparent Truth
It might be obvious, but the way you attract new clients is not by using your name or showing off your bank account. It is by placing what you do on a display. It is unlikely that someone will hire you without knowing if you're capable of crafting beautiful imagery. This is why it is of great importance that your business is supported on those two pillars: fresh portfolio and your financial profit.
That Special Client
If you haven't worked with that kind of client, you probably will. They may require you to sign a ten-page non-disclosure agreement that you're not going to use this work in your portfolio, nor will you mention you've worked with them. Other clients are simply asking you to not publish their images or videos. It is quite an unpleasant feeling to hear such a demand in case the project turns out to be highly successful for the client or is some of your best work nobody will ever know you were the author of.
Saving Yourself Some Trouble
How would you react in this situation is up to you, but if you don't make your policy clear before confirming your participation to the project, you better accept the fact you won't publish it and pass on. It is very unprofessional to argue your right to publish your work, because you've taken it for granted. The client has rights to refrain from granting you permission to. This is where your policy has to be clear during the negotiations.
Charge More, Pass On, or Don't Care?
There is no definite answer or a formula on what's the best policy. I will give you my personal opinion on that and how I would react in such situations.
If it's a big client, I would charge more in almost all cases. I would not if I decide that they would pay me enough anyway or that working with them would bring me indirect benefit by creating new valuable connections.
If it's a client who wants to do something that I'm not that eager publish, I may not raise the price as well. Let's say you shoot headshots on a white background and you have more than enough of a variety to display in your portfolio and a new client comes demanding their headshots won't show up on your website.
Not accepting a project, because you can't publish it is not something I would consider and I've never did, but it is also an option for those who want to have everything they do published.
How Do You Tell It to the Client?
Of course, I'm talking about how you're going to tell the client that you're charging more in case they don't want their photos or videos published. People are different and it's good to stay positive and know how to ask for more without offending your potential client. Stating your charge more in case your work is not published right from the beginning is not a good option. They may have never thought they have the power to forbid you. This is why I usually ask if they are fine that I publish one or more of the final products they will receive. I am clear that this will only be from the work they purchase, because they will know if anything gets published it is what they actually like. I will also explain that this is what brings me more clients, not just the money I receive. I also tell them that by default I don't put other personal information of theirs unless they want me to (for example in the case of a business headshot, mentioning them and their company might be beneficial). Most people would gladly agree to grant you a permission to publish that work in your portfolio. In case they say "No," I would tell them I am charging extra. That wouldn't sound surprising, because they already know it is the fresh portfolio that brings me clients.
Charging more for not being allowed to publish some work should not be an exclusive policy. Although backed up by sound business facts you might lose a potential client. Let us know in the comments if you had such cases, what you did, or what is your business policy in such cases.