Political labels are always subjective at best, but you also need to look at the long tradition of Russian Czars who add adjectives to the end of their names - Ivan the Terrible, Catherine the Great, etc. Perhaps he was just doing it to fit in?
From a historical standpoint though, Peter the Great did have some quite notable achievements towards the modernization, growth and stability of Greater Russia. He defeated Charles XII army from Sweden and established a city on the River Neva - St. Petersburg, conquered the Cossacks of the Crimea, defeated a Turkish armada, and established control over the power of the church (or at least met its challenges to his authority). These could all be called accomplishments worthy of being "great" in Russian eyes, especially when considered in the historical context of the time.
This is, of course, a matter of opinion.
If you wanted to argue that he does deserve it, you would say that it is because did a great deal to modernize Russia. By traveling through Europe, he saw many new ways that he brought back to Russia. Most of these were technical things that were meant to increase Russian military power. Partly by doing this, Peter managed to acquire a great deal of new territory for the Russian Empire.
To argue that he doesn't, you should point to the fact that he did not really do much to help his people. He tried to take all the power for himself (ended representative government) and did not use his modernizing to help the people. For example, the modernizing of the armed forces actually hurt peasants because it increased the amount of taxes that they had to pay.
Why did they call peter the great peter the great
Peter I (1672-1725 AD.) who became king of Russia at the age of 10 and assumed supreme power in 1689, definitely deserves the title of "the Great" from the perspective of Russia.
Peter gained access to sea for Russia and played a major part in modernizing Russian culture and institutions. Prior to Peter Russia was an isolated agricultural society. Peter transformed it in a powerful modern empire.
However, the methods used by Peter for modernizing Russia were ruthless and oppressive. Because of this he has also been widely criticized. Also, in the process of modernizing Russia he may have also caused avoidable harm to Russian culture.