I've always assumed Wendy meant to be A Wendy. Peter Pan took Wendy to the island to be a "mother" to the boys and tell them stories. Peter felt she "betrayed" him by growing up……BUT Wendy had a daughter. Peter took HER to the island to be a "mother" to the boys and tell them stories. He did the same with HER daughter when she grew up.
So, it may mean to be "A Wendy", one of many!