Gotcha Day. While I'm not sure that's the name I'll refer to it as, it is a very common phrase for the day that the parents meet their child. I use the term to search out blogs, as well as YouTube videos. Like I did when I came across this video that an adoption agency (CCAI) put out to show what "Gotcha Day" is. I'll let the video do more explaining, while showing you what it looks like as well.