It all depends on your country of Jurisdiction. I live not far from you in Cyprus and the tax laws are quite healthy here and our thoughts are the same to open a limited company here. Check out what the capital gains tax or corporation tax is in your country and what banks facilitate a business bank account, then once you open a business bank account and get your accounts audited, you should have no problems with the rest. Good luck in your endeavor. 

Actually there's no bank who really tie up with cryptocurrencies because they think that cryptocurrency is one of their competitor when it comes of money.
In our place lately all bank account related with cryptocurrency was totally banned there are some bitcoin users  has a suspicious account, and now our bank here were declared banning for those account who involved in bitcoin transaction, so it is impossible that you have create bank account and used bitcoin to convert fiat. Here our place there some remittances who accept bitcoin then convert to our local fiat.

Examples please? I've spoken to multiple people about opening a bank dealing in crypto and they were more than willing too. At the end of the day if they are receiving fiat in your account then they can use that just like anyone else. Cryptos aren't killing banks due to a lot of people cashing out crypto to get their money into fiat.

So please give me some names because every single top banker around me is willing to accept customers that are dealing in crypto but depositing fiat into their account.

Israel is part of the country that support crypto currency due to news of their country wanted to issue their own coin. I suggest to get information from banks that support the SEPA but Graft Network features is good for your business though.

Banks are already on an open war against bitcoin and cryptos. So no bank will allow you to open an account if your company is related to crypto business. It is better to start a shell company in some other name and some other business and transfer the money in to that account. If you declare openly that your company is into crypto business, banks may first open your account but can later freeze it with your money. Otherwise prefer paying out salaries in cash or pay order. Banks hate crypto currency so they won't help you in any way.

I am not sure what are all the banks will support digital currencies trading. You will get the more details by surfing about that in google search in your country. If citi or axis banks gives support in your country go direct to the bank manager in your city and asking for digital currency current account. You may get the proper guidance from these banks.