I don't know if this works well as a name but there is Vermilion.
Ginger, i had a dog named that. lol
The Irish for red is dearg, but when referring to red hair it's "ruadh" so maybe Rua or Rue? I suppose that's a tie in with Ruby too!
Rose and its variations—Rosa, Rosie, Rosalie
Coral and its variations—Cora, Coraline, Coralie
Good luck, I hope this has helped! :)
Love Cassia, Cherry, Coralie, Rosalie, Poppy, Rue, Rosamund, Ginger, Phoenix (particularly love this suggestion!), Seraphina and Seraphine and Rose of course too! Gosh you berries are good!! Thanks everyone!!!
Might be too out there but I like
Mira- a red star
Ronan and Rowan for sure! And also Poppy and Sorrel.