If you accept that the contract for professional accountancy services is against Y and not X you will have to discontinue against X and reraise the action against Y. You will be liable for X's costs.
The relevant issue is with which entity the contract for professional accountancy services was with. The fact that they wrote to a different entity afterwards doesn't matter. There is no ambiguity about for whom the work was done presumably.
Which company issued a terms of business letter to yours?
Yes you are.
If the wrong party is sued there is no doubt it would be struck out although it is normal for a defence to be stated as well.
Yes, they are two different companies.