According to the Graffiti Diplomacy website, the best way to uniquely express yourself in a graffiti tag is by understanding tagging alphabets and choosing a catchy tag name. This name can be a real name or a nickname.
The site notes that it is important to study tagging alphabets. Tagging alphabets are standard alphabets, but the letters are all written in a unique and visually exciting style. Choose one of the alphabets and practice writing out the letters. The site recommends using a wide magic marker if possible, though pencils or crayons can also be useful for practicing freehand on a sheet of paper. Pretending to write the letters in the air may offer a better idea of the motions required to paint the letters on a wall. After sufficient practice, pick a unique tag name, and practice writing it in the style of the alphabet chosen. The site notes that learning to write the tag name well takes a lot of practice. It is best to have a large stack of white paper before practicing your unique tag name. Try to add variety to the tag style by stretching certain letters out or replacing parts of letters with symbols. Experiment with writing letters in different sizes. According to Graffiti Diplomacy, the finalized tag should express both movement and style.