So... this one gets silly becaue of the goofy naming
Ranni is the Lunar Princess, allegedly a daughter of Radagon and Rennala. And a demigod. (Radagon is a full god, because Radagon and Marika are some kind of split entity.
Radagon married Rennala whose is the Queen of Raya Lucaria and the Academy bossfight to end a war between them and Leyndell.
Ranni uses the name Renna when first meeting us, presumably as some sort of alias because the Tarnished are generally mandated to hunt down the demigods for their rune shards.
Actual Renna is a Snow Witch who either raised or trained Ranni in magic. Seemingly she was part of the Carians who were being attacked at their manor by Rennallas Cuckoo knights, so theres some sort of strife there.
Noticeably, Rykard and Radahn, Ranni's brothers have runes. Ranni does not appear to have one.
This would imply that either Rannis rune is the one you get from Renalla, or she was never given one for some reason. So she may have already been in hiding when the Shattering occurred. (Miquella also doesn't have a Great Rune apparently, or at least we never need it to repair the Elden Ring, so maybe the twins shared one)
This would indicate potentially that Ranni was born, went to learn Carian magic. But then the Carians rebelled and kept her from getting tied up with the rest of the Golden Lineage before the Shattering occured.
Theres another bit of weirdness where Ranni is also an Empyrean, which are children of a single god who are destined to become gods and have Elden Lords as consorts. Melania and Miquella are as well, being born of Radagon and Marika who are one person. But theres no indication on who Ranni's parent would be, other then this would mean not Rennala. Possibly another outer god designates her, because we see her fingers in the background when we finish her quest (Very very dead because we gave her Fingerslayer), but not how many fingers they have, so it could be another case like the 3 Fingers and the Frenzy God.
Melina is also identical in appearance to Rannis physical non-doll form (and the spectral form on her side) and shares a VA. So Ranni and Melina may be a split aspect similar to Radagon and Marika. Still leaving their parentage unexplained though. They could potentially be offspring of Marika of course, who was actively defying the Greater Will by removing the Death Rune and being eternal, even while still stuck inside the Erdtree.