Looking for a big company when it comes to deploying brand new blockchain and it's coin
Why don't you just try to deploy your own blockchain and use auditors to audit the code? If the problem was about the security and this can be done through auditing your code to the company like certik or hacken.
Feel free to write the companies name whom you can trust when it comes to giving them reasonable projects. ( Blockchain, coin, erc20, ICO)
I know some companies that offered service for ERC20 creation but I never saw service for the blockchain creation as it needs a lot of resource as when you re creating a new blockchain and you must have created various variables just like wallet, explorer, etc. I remember the name was tokenmarket but I don't know whether this service is still exist or not caused by so many developers issued their own token without the help from the service. The majority of developers were doing self audit.
because security is my main concern.
This can be done easily just send your code to the certik and certik will help you to find bug or backdoor. The only problem is whether you can afford to buy the service caused by the security audit will need a lot of money to be used to pay the service. It's not free service.