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What you are talking about it is a Facebook feature called "tagging". Once you have the individual or group photos uploaded to your Facebook page, they can then be tagged.
Click on the picture that you want to add peoples names to. Once it opens up into the large framed mode, you will see an icon on the lower left can that says "tag photo". Select this option and then click your cursor over the individual that you want to add the name. A box will open up that allows you to type in the name of the person.
When this is completed, the name of the person will be highlighted when the cursor is moved over that person, but it does not provide a link to that individuals personal page.
Feel free to post any follow-up questions you may have.