Setting up limited company after signing first contract

I am working full time and pay tax on PAYE basis.

To supplement my income recently I have started working on a project as a self employed contractor for an organisation (not related to my full time job). Having giving it some thoughts I have decided to set up a private limited company for my contract work as it would be beneficial for me from a tax perspective.

However I have already signed a letter of engagement using my own name with the organisation (though I will not be paid until later on this year). If I set up my company now, will I need to sign a new letter of engagement with them using my company name or will my current letter of engagement be fine as I can say I signed it in my capacity as the director of my soon-to-be-formed company? The organisation has made it clear that they would be happy for me to submit the invoice through my company so my question is really from a legal/tax perspective.

Thank you.