I was adopted in St Louis. My adoption was in the legal paper which you can view in the city library on Olive. I believe there is a county paper as well as the city paper. I go every Sat to try to find my brother's adopted name.
The notice is in Notices to Parties to Appear in Court
It has a heading In Re: -------- ---------, with my birth name in the blanks. The birth parent(s) are notified and named that the petitioners (my adoptive parents are named) are going to adopt the child unless they appear. My notice was within a couple months of the actual adoption and had to run 4 times.