Have a purpose. More than just, “erm, do magic”. Are you flaunting your strength? Making money? Gaining leverage? Are you all from one banner? are you secret? do you let anyone in or are there strict entry requirements?
Have a schtick, something that makes you recognisable if seen ritualling - oh its that blue robed Winter lot; it’s the morris dancers, oh no, its the noisy Freeborn again. Think about a common visual element - put on your wizzard hat, red scarf, tabards, a white ribbon tied on the left sleeve. Easy if you’re also the same banner, but very doable if you choose an accessory that fits for most people’s kit.
Think about how you express the elements of your hearth magic - do you meditate? Sing? do jumping jacks? reach for the non-existent lasers? Do you make heavy use of props (staves, orbs, robes; but also maps for divination, models for resources, swords to bestow battle buffs)? Do you speak chorally, or just one of you, or each in turn? Do you move precisely, chaotically, rythmically, onto and off stage, together, follow-my-leader? Could one at a glance distinguish the target (s) of your rituals from the contributors, or do they act the same?
Example: Brass Coast hearth magic is coins, contracts, fire (theoretically) and music. Our is a family coven, and we sing - big, loud, not neccesarily well, and involving everyone - mages, other family members, small child, guesting NPC, people waiting for the regio … A different song for each ritual. Lots of shaking of whatever one is holding - tamborines, staves, ribbons, a covenstone. Targets get a verse aimed at them - and everyone waves their implement at them. Every makes a lot of noise - brazenly, in fact.
Oath - think about what is your coven for? Do you usually just enchant your banner? Are you into big army rituals? Are you for hire? What realm(s) do you cast in? If I overheard the oath being administered, I should have an idea what that coven are all about. One idea to make your oath central is to begin (or end) rituals with reciting it. If you plan to use it often like this, make it short. Something a bit poetic makes it easier to remember.
Example: "Passion and Profit ! Family and Empire ! Wherever we stand, we are Freeborn ! "
(it really does sound out those exclamations)
Oh, and rainbow covens are much harder to organise. Pick one or two realms and half a dozen mastered rituals you can do well, rather than be a bit ok at everything.