Does “The Great” belong after Alexander the king of Macedonia’s name

Does “The Great” belong after Alexander the king of Macedonia’s name? One of the greatest and most successful generals in all of history was Alexander the Great. He was a brilliant, patient and often devious man that never struck without careful planning. Alexander make decisions with great speed and took big risks. People described Alexander as the son of Zeus.
Firstly, Alexander is responsible for spreading Greek culture. He founded various cities. People considered him a “philosophical idealist” with his policies of incorporating various races into his military and government. He was never defeated in battle. At the age of 32 he controlled an empire that spanned from Greece to India.