Margarita is right about Alexei’s official title : since Emperor Paul 1st , who was the first to write a Succession Law (in 1797), the Heir to the Throne's official title was: “Heir, Tsesarevich, Grand Duke and Imperial Highness” (see the 1886 Law on the Imperial Family, #19.1 or the 1906 Fundamental Law, #144.1) . As the older title of Tsarevich could mean any son of the Tsar, a new title - Tsesarevich - was to be used solely by the Heir to the Throne. Official documents referred to Alexei as “His Imperial Highness the Heir Tsesarevich and Grand Duke Alexis Nicholaevich” (Ego Imperatorskoe Vysochestvo Naslednik Tsesarevich i Velikiy Knyaz’ Aleksei Nikolaevich), which should be pronounced somewhat like – stressed syllables underlined: Yevo Imperatorskoye Vissochestva Naslyednik Tsyesaryevich i Viliki Kniass Alyeksei Nikolayevich).
As for the title of “Gosudar” (usually translated as “Sovereign”), it wasn’t part of the official (legal) title. I have seen this title used in some documents regarding Alexei, but it was usually reserved to the Emperor and Empresses. Official or not, it seems Alexei liked it as he once made a fuss about it. In her memoirs, Dr. Botkin’s daughter Tatiana mentions that on one of his brother’s portfolios of drawings he sent to the young Tsarevich Alexei, Gleb Botkin had omitted the word Sovereign (Gosudar) in his dedication and written “To H.I.H. the Heir Tsesarevich and Grand Duke Alexis Nicolaevich”. According to Tatiana Botkin, the Tsarevich insisted that Gleb Botkin use the more courteous form of address “H.I.H. the Sovereign Heir Tsesarevich and Grand Duke...”(Gosudar Naslednik i Veliki Knyaz).
I might add that, except in official documents, the Tsarevich was usually referred to as the “Heir Tsesarevich”, even in writing, and that the less educated Russians refered to the him simply as ”The Heir” (Naslednik).
Mandie mentions chivalry orders and military titles Alexei held. They weren’t part of the official title of the Heir to the Throne but were rather honours bestowed by the Emperor. On the day he was born, Alexei was named Ataman of all Cossack Troops (cossack title for a military chief ). On the same day he was also named “chief” (shef) (similar to the British “colonel-in-chief”) of the following regiments:
- Atamansky (Cossack Cavalry) Guards Regiment of His Imperial Highness the Heir Tsesarevich (by tradition, as Ataman of all Cossacks, the Heir to the Throne was chief of this regiment, but only until he became emperor);
- Finlandsky (Infantry) Guards Regiment;
- - 51st Litovsky Infantry Regiment of H.I.H. the Heir Tsesarevich,
- 12th Eastern Siberian Rifle Regiment of H.I.H. the Heir Tsesarevich.
At the same time he was enrolled in all regiments of which his father, mother and grand-mother were Colonel-in-Chief at the time.