Here is a very simple to create activity for very young children. I think I started this with L when he was about 9 or 10 months and he still loves it at 15 months. I got the idea from his school. They took a plastic container and cut a slot in the lid. Then the child can slide in baby food lids or some other small lids. For added benefit, you can add photos of family members, classmates or anyone you would like your baby/toddler to learn their names.
This was L's favorite activity for the longest time and he still plays with it once in a while.
You can also make a sort of family tree with circles just big enough for the lids so the child can match the person's name to the picture for older children or you can put a photo on the family tree for younger children. I love this idea because it allows children to see how family members are related in a very tangible way. It is hands on and hopefully more meaningful. And maybe they will even be less shy around the family because they are used to seeing their photos.