The Greek alphabet has been used to write the Greek language since the 9th century BC. It has 24 letters, many of which English-speakers can recognize. The letters that English does not possess are the Phi, Chi, Psi, and Theta. All the other letters neatly correspond to a single English letter, although many of the Greek letters are not written the same way as their English counterparts. For this reason, writing your name in Greek is as straightforward as learning how to write the Greek letters that correspond to the letters of your name.
Visit the Greek Alphabet website in the Resources section.
Look over the list of Greek letters and note which ones correspond to the letters of your name.
Print out the list of letters.
Place blank paper over the list and trace the letters that correspond to the letters of your name, paying special attention the movements of your hand needed to make the letters.
Practice tracing the original printout until you can write the letters on your own. Practice writing these letters until you can write them fluidly, just as you can write your name in English fluidly.