Hi Hsir262 and welcome.
I would strongly advise you NOT to trade through the limited company. You should each have your own separate businesses. As well as setting up a limited company together you also need to set up your own business and separate business bank accounts. Pay your takings into your separate business accounts, not into the joint limited company.
If you each also have your own limited company that you put your takings into, you can take a small salary - enough to qualify for a state pension and other benefits and pay yourself dividends out of the profits. It’s a more tax efficient arrangement and perfectly sensible as you won’t know your annual earnings until the end of the trading year. It will cost you more in accountancy charges so only set up a limited company to trade through if you expect to pay enough tax for this to work out as a good deal. You may be better off operating as a sole trader.
If you put all of the takings into the joint company it’s not going to work. As 50:50 directors you will both be entitled to half of the profits even if one of you is ill, pregnant or otherwise unable or unwilling to do an equal share of the work.
Another problem is that you are likely to have to charge your customers VAT if you trade as a joint enterprise. If you each work solo and share the bills you are much less likely to reach the turnover threshold. Charging customers VAT makes you more expensive than sole traders and increases your accountancy charges by quite a bit because it’s a lot of work to prepare VAT returns.
Treat the limited company as a salon management arrangement and pay money into the limited company to settle the bills. Don’t draw any salary from the shared business, just take dividends split between you if there is a profit. There will only be a profit if have other people paying you rent - this money belongs to the limited company who will be responsible for settling all the bills.
Your accountant will be able to talk you through this, take advice from an accountant who has other salon clients.
Good luck.