The answer to this is that we simply do not know what happens at the Ceremony of Two in The Giver. Some of the ceremonies are described in the book, but others are not. The Ceremony of Two is one of the ones that is not.
The only thing that we are told about the Ceremony of Two is that Jonas found it boring. We see this on p. 57. In the pages before that, we got a description of the ceremony in which newchildren are given to their families. Then we are told that Jonas
sat politely through the ceremonies of Two and Three and Four, increasingly bored as he was each year.
This is the only time that the Ceremony of Two is mentioned in the book. Therefore, we really do not know what happens in this ceremony. If we assume that it is like the other ceremonies, we can infer that Twos receive something that signifies their new age. It might perhaps be something that has to do with learning to walk, but that is just speculation. Do you have any thoughts about what children might get at their Ceremony of Two?
No, sorry, I don't have any thoughts about what they might get. Thank you for your help :)