There are 5 codes used in the movie for Russian moles in British Intelligence: "Tinker" for Alleline, "Tailor" for Haydon, "Soldier" for Bland, "Poorman" for Esterhase, and "Beggarman" for Smiley. Why were the latter two not referenced in the title?
The title isn't a reference to the characters' codenames, but rather a play on words of an old rhyme (from which the codenames are also derived).
The most common adaptation of this rhyme comes from A. A. Milne [the chap most well-known for writing Winnie the Pooh] in "Now we are Six"
That version starts…
Tinker, tailor, soldier, sailor, rich man, poor man, beggar man, thief
The original novel, by John le Carré, 1974, and the movie, simply make a play on words of the first four characters.
Sailor is replaced by spy, rich man and thief are also absent from the title.