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If I want to write for example "Mr. K". I don't want to use just a single letter. Should I write it like "Mr. Kei", "Mr. Kay" or "Mr. Key"?

Update:

Let us imagine there was somebody with name Mr. King given at birth. He doesn't like his surname, but he likes when others address him as "Mr. K". So, he wants to change his surname. But he doesn't want to use just a single letter - it is too short. So is "Mr. Kay" the right way for his purpose?

If you write it any other way than "Mr K." it will not get interpreted as "Mr K.", but as another name. ('Kay', 'Kaye', and 'Key' exist as English surnames anyway).

Every letter in the alphabet has a phonetic spelling, and these can be found in dictionaries.

For the letter K, the phonetic spelling is kay.

kay (n.) the letter k

However, I must echo what others have already said – if you are sending a letter to someone whose last name begins with K, the convention is to use the initial, not the phonetic spelling of the letter:

Dear Mr. K,

I’m writing to thank you for the help you gave me the other day.

As Hot Licks mentioned in a comment, this is typically considered an informal form of address, although I have seen a few exceptions, like when someone has a very hard-to-spell last name, and therefore as a general rule prefers to go by, say, Mr. C. or Dr. H.