In transliteration, the letters and sounds of one alphabet are converted to a different alphabet. Most languages have at least some sounds that are unique or complex, and may not easily be interpreted by the letters and sounds in a different alphabet; thus the sometimes confusing look of diacritical marks, dipthongs, etc. in the new venue. If you listen closely to comedians or others imitating "foreign accents" you'll see the kinds of substitutions they make to approximate the particular sounds which have no equivalent in the original language, and thus sound "funny" to we who speak the English language (the latter a fact which some Brits may not quite acknowledge).
Take the Russian name of the famous composer of Swan Lake. It has been transliterated into Roman letters as Tchaikovsky, Tchaikowsky, and Tchaikovskii. (In other Western languages, it may seem unpronounceable if you don't know the language, e.g. 'Piotr Ciaikovski' in Italian.)
Take the city that in the West has been known as Piraeus for many hundreds of years, derived from the classical Greek name. In Modern Greek, the same classical spelling if transliterated directly from the Latin/English would now be pronounced 'pirefs'. What was the letter beta (β) is in Modern Greek pronounced 'veeta'-- and to get the 'B' sound, you have to write mu-pi (μπ).
Time ago, both Roman Catholic and Greek Orthodox missionaries worked among the Albanians, and both tried writing prayers and parts of the Gospel in the two major Albanian dialects (Tosk or Gheg). The Catholics wrote with Roman letters, and the Orthodox with Greek letters. If one compares the same Albanian text as transcribed by both groups, it becomes obvious that the missionaries not only spoke different languages, but heard with different ears!
In searching LINUS by author or subject, there should be some good cross-referencing to direct you to the spelling used as the official heading. For example, the name of the famous Cretan author of The Last Temptation of Christ is usually spelled 'Nikos Kazantzakis'; in the catalog, it was 'Kazantzakēs' for a long time, but has now finally been changed to 'Kazantzakis'. However, Odysseus Elytis (or sometimes Elitis) has the heading Elytēs, Odysseas, 1911-1996 . And, just to complicate matters, some other modern Greek authors have changed their own names. LINUS will guide you by cross-reference to the spelling used in the catalog.
If you are trying to be comprehensive, whether searching databases or LINUS, try performing a Keyword search using the OR operator option between the variant spellings you may have seen. This will capture the variant spellings in titles, notes, chapter headings in tables of contents, etc., since the author of the book or article may have used a variant spelling.
And, of course, you can always seek the help of a Reference librarian to be sure you're getting what you're after.