'It's a name' needs to be substantiated by actual use. Where is it being used? How widely? How popularly? I might name my child 'Qumquat' but that wouldn't make it an established name, just a single occurance (of questionable sanity).
Paean is actually from the Greek Paian and meant 'hymn of thanksgiving to Apollo'. Paian was the Homeric name for the physician of the gods in the Greek pantheon and just invoking his name was praise to the healing and power of Apollo.
I have a feeling that modern use of the name is based on it's contemporary meaning with total ignorance of it's true etymology and pagan meaning. I daresay it's limited to devout Evangelical Christians who would be appalled to know their child's name sends up praise to Apollo each time it's spoken. If we included the true etymology, we might just nip that 'it's a name as well as a word' thing right in the bud.