Alright, firstly – the specific word used for Baby Chen here is "Ekechen". This seems to be an online slang to describe a baby. I guess it's cuter than the usual "Akachan".
Next – I'm just guessing for the Present Chen here, but it works – assuming that it's really "genjou", what Murai used for the "gen" part here is 幻, which means illusion and the very same "gen" in Gensōkyō.
