Tolkien coined the name Wanōna (also Welinōre, Wanōra, Oanōra) in his Story of Kullervo. It's totally possible they belong to Tolkien's constructed languages. But I think the etymology is still interesting.
*** Thanks to Yellow Sky's comment. Now that it's not a name in the original, the following older content isn't relevant any more. But I'll keep the finnish label just in case.
I came across this name in some articles on Tolkien's works. Kullervo is a mythical figure from the Finnish saga Kalevala. The articles claim that Kullervo sister's name Wanona means "weeping" without adding a reference. All that I can find via searching "Wanona + Kullervo" are articles that are really about Tolkien's Legendarium, which raises some doubt in me.
It's known that Tolkien took much of Kullervo's story into his Children of Húrin Saga. SPOILERS?. The main hero, Túrin, married his lost sister Nienor unknowingly, and both committed suicide when they found out the truth. Same tragedy happened to Kullervo and his sister. Nienor's name is in one of Tolkien's artificial languages, meaning "Mourning". It'd be another interesting parallel if Kullervo's sister is indeed called "Weeping".
But I can't seem to find the name Wanona in the Kalevala texts that are available to me. I know little about Finnish, so it'd be a hopeless task for me to look it up in Finnish sources. It looks like Finnish words for "weep", "mourn" are nothing like Wanona.