There are actually a number of words for this, depending on the context. I'll try and give you a feel for the ones you have mentioned as I understand them. FYI, I am an American and these words sound likely to be used slightly differently in the UK.
a laissez-passer: This is French, not English. The UN does a lot of business in French, so that is the likely context. Before your question I had never seen nor heard this combination of words. Exceptionally rare.
a pass This is a common and general word, especially used with documents that allow limited-time access. It is also often used for a sticker or tag that allows you to park your car somewhere. A "parking pass." A parking pass would likely be hung from your rear-view mirror.
a permit Similar to a pass but perhaps slightly more proper/formal. You hear "parking permit" a lot. A permit is likely to be something that lasts for longer, like a year-long parking permit, which would tend to be a sticker in your car window. Normally I would not use "permit" to refer to something that gave me access to a building or venue, but I wouldn't think it's an odd usage if someone else did.
an access badge is something you clip to your shirt normally that gives you access to a secure area, perhaps a government building.
When people have permanent passes, they often have names for them that everyone else in the organization uses. For example, an "I.D.," a "badge," one's "card" or a "tag" might be understood unambiguously by people in a particular organization, while these may have a different meaning in the general population.