Yes, you can pot them up individually as gifts. It's best to let the offsets grow to about 5" tall before separating them from the parent plant. When you dig them to separate, some might not have roots of their own yet, but that's okay. Aloe Vera roots easily. Just pot them up, but don't plant the stem deep in the soil. You could even just set them on the surface of the soil and set rocks or other things around them to hold them upright until the roots form. I like to plant them about 1/2 to 3/4 inch deep, though.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams