In addition: and Aleksandr III. All these tzars ruled in 19th century. Aleksandr I and Aleksandr II are known as reformators and charismatic and versatile personalities. Aleksandr I won against Napoleon Bonapart. Aleksandr II emancipated the serfs.
This name is very widespread among the Russian men. I think the most of people in Russia have 5-10 acquaintances or friends named Aleksandr. Personally I don't like this name because it is very popular in my country.
Aleksandr has almost hundreds of nicknames, pet names and diminutives, including - Sasha and Lyosha, of course, but also Shusha, Shuya, Shurik, Sanya, Shura, Leksa, Alek, Alechka, Alchik, Leksya, Sanik, Shanik, Shasha... and many more, for various levels of friendship and familiarity.
My favourite is Shurik. It was made famous as the nickname of the protagonist of a Soviet comedy, and many Aleksandrs of that time wanted to be nicknamed Shurik, or so I'm told. A teacher of mine has a son named Aleksandr they call Shurik, and he's named for this protagonist.
Aleksandr is very, very common in Russia. Moreover, apparently it's bouncing back as an extremely popular name choice for Russian baby boys.