If you do mean Tengwar, the link below shows an image of the symbols of how to write it.
That question is not readily answerable, as there are several scripts used by the Elves (although you probably mean Tengwar), and those scripts again have several different modes of writing depending on when, where, and by whom it was written. I would suggest further research, or to ask in a reliable forum etc. However (as it is apparently a not so uncommon error): do not try to type "Legolas" and convert it to a Tengwar/etc computer font, as this only results in gibberish.
NOTE: Legolas (Silvan), Laegolas (Sindarin), Greenleaf (English), so Legolas already is Elvish.
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His name is Legolas. Tolkien did not tell us any other names. The "Greenleaf" sometimes added to his name is merely a translation of his name. ---- Legolas' name is Legolas, sometimes Legolas Thranduilion "Legolas son of Thranduil" and sometimes Legolas Greenleaf, though the correctness of the latter is debatable. Legolas was played in the films by Orlando Bloom.
Orlando bloom plays Legolas
Runya is the word for flame in elvish.
Legolas was his name.
Legolas is a fictional character in J.R.R. Tolkien's The Lord of the Rings. He is not a real persona.