Wave the hand is a common gesture used to convey various emotions and messages. However, there are several other words that can be used as synonyms for this gesture. One of the most popular synonyms is 'flap', which refers to the movement of the hand up and down. Another synonym is 'gesture', which implies a movement or motion that conveys a message. You can also use 'beckon', which means to signal someone by waving your hand in a specific way. Additionally, 'salute', 'greet', and 'wave goodbye' also imply a waving of the hand. Ultimately, these synonyms can be used to add variety and color to your language and communication.