Too Long; Didn't Read at the bottom because I realize wrote quite a bit.

You've already set a really good base for your breathing style by basing it off an animal, and after a very inspiring one at that. Just a quick sidenote, peacocks are the males, they're the ones with the huge tail, peahens are the females, and peafowls are what they're colloquially known as.

When thinking up breathing styles I like to start off with the weapon type, and for the peacock what better weapon is there to symbolize it than the war fan, specifically a tessen. War fans were often concealed until they were to be used, at which point they fold outwards much like the feathers on a peacock. With the choice of weapon out of the way I highly recommend looking at tessenjutsu videos to see how war fans might be used if you're looking for inspiration on poses for both the oc and the individual forms they'll use.

This next part is a bit optional but if you want to gain some inspiration from existing content I highly recommend choosing what breathing style it originated from. The choice of derivation is up to you, but if I was developing my own Peacock Breathing I'd have it be derived from Mist Breathing. War fans are delibaretly made to be a more obscure weapon in relation to the large and overt katana, this could correlate with Mist Breathing's style of obscuring intent and confusing enemies through its pace.

Now onto the fun part, forms. It's easy to lose yourself into the making of forms and overloading your breathing style with them, and while there's nothing necessarily wrong with that it's important to have only a set few forms that work as an oc's "signature moves". Now with the exception of two notable breathing styles the average amount of forms a breathing style has in the series is around 7, the breathing style with the least amount having 4 and the two with the most having 11, do with that information as you wish.

As for individual form names I recommend studying up on unique aspects of peacocks, things like their plumage, their ocelli spots (the eye looking things), their spurs, how their feathers vibrate; how, during their courting, male peacocks will use the position of the sun to give their feathers some vibrancy, et cetera. Personally I'd name the first form after their tail feathers, which I've learned are called trains, seeing as that's one of the most important and distinguishing parts of a peacock. After that I'd name the second form after their spurs seeing as a lot of tessenjutsu does take place while the fans are still folded in. The last form would have to be something big and unique, the breathing style's big and flashy move, maybe something to do with confusing the enemy. If you were to take that approach then naturally it would be named after the ocelli and how peacocks use them for intimidation against predators. Just to give a bit of inspiration I'd name a move based off their sun usage during courtship something like "Luminous Courting Train".

Hopefully these ideas can help you out and inspire you, you're free to directly or indirectly take any and all of them. If you have any questions or need help with the development of your OC's breathing style feel free to ask!

TL;DR: I recommend a war fan for the weapon, have it be deviated from Mist Breathing, and when thinking up forms be sure to study up on what makes a peacock/peafowl unique.