This name was used by Giambattista Basile in The Pentameron (Pentamerone, Tale of Tales), written in the 17th century. Basile was a Neapolitan poet, soldier and courtier, his sister Adriana was a composer and singer, and her daughter Leanora inspired John Milton when he heard her sing in Rome. His sister helped him compile the folk tales and fairy tales, which is what he is now best remembered for. He recorded and modified the tales in his local dialect, putting them into two volumes. The Brothers Grimm in fact used some of his work, including Basile's versions of Cinderella, Rapunzel, Puss in Boots, and Sleeping Beauty. The title Pentameron was given because Basile's writing was arranged in the same manner as Boccacio's Decameron.
*Spoiler alert: if you haven't read The Merchant and would like to, revisit this page later*
In The Merchant, Menechiella is a princess living in a kingdom where a seven-headed monster has taken over, demanding one human for dinner every day. When it comes time for Princess Menechiella to be eaten, the kingdom is very sad, and yet no one has any solutions. A passerby, Cienzo, a merchant's son who has a kind heart but had an unfortunate accident, bravely slays the monster and returns Menechiella to her father. Instead of sticking around to claim a reward, he goes to the tavern to wallow in self-thought. The king wants to reward the person who saved his daughter, but, not knowing exactly who it was, sends a messenger to find him. Then, a local man takes the opportunity to claim the reward (since Cienzo hadn't yet). The king is overjoyed and gives the man his crown. Cienzo, hearing the news, informs the king and his daughter that they've been wronged. He is married to Menechiella, and all should end happily, yet the next morning he sees a beautiful woman in another house and goes to see her (by sneaking behind Menechiella's back). This beautiful woman happens to be a sorceress and keeps him there, while Cienzo's brother Meo travels to figure out what happened to his sibling. Thinking that Meo is her husband, since the brothers look so alike, Menechiella spends the day with Meo and they go to bed together (platonic), and the next morning Meo finds out his brother is being held captive by the sorceress. He kills the sorceress and begins to tell Cienzo about the previous night, in bed with Cienzo's wife, and without listening to the full explanation Cienzo cuts off his brother's head. However, once his wife explains in detail, Meo is pretty much magically reanimated, and they all live happily ever after.
It should be noted that, as an adult-only story, it is very humorous (in my edition, at least).
Menechiella is not a baby name that has been used, although Menechella and Menechiella can be found as surnames. There is no recorded meaning.