I need some help in why you need to use 'Yours sincerely' when you do know the name of the participant receiving the letter and 'Yours faithfully' when you don't. To simplify it what is the history or reference that set these rules in English language.
In 1926 in "Modern English Usage" page 332, H. W. Fowler listed these phrases and their uses:
Yours faithfully (to unknown person on business) Yours truly (to slight acquaintance) Yours very truly (ceremonious but cordial) Yours sincerely (in invitations and friendly but not intimate letters)
What we write at the start and end of a letter is not dictated by rules, but rather by convention. When, having never met you, I call you Sir and later assure you that I am your faithful servant, or call you by name and later assure you that I am your sincere friend, it is understood by everyone that I do not really mean these things. I am being 'conventional'.