Will the nickname be called "small" if you click on it?

No.

Children are usually given nicknames when they are very young. The child is very small when he is a child, giving people a feeling of being small and cute.

The baby's baby name "Dian Dian" is given directly using the word "dian", which gives the baby a more petite, cute and personalized feeling, because this word is not a common name.