His name I guess is Andreas Di Lecce-Komnenos Drakos, but if he manage to make it until the coronation he would be Andreas III Drakos of Rhomania and Andreas II Di Lecce-Komnenos of Sicily.
I've some doubts about the numerals of Sicilian despots (Do they include their time as Dukes of Abruzzi?), but this problem would only apply to future Alfredos and Manuels.
I've got a doubt about Andreas' father, Alexios since he is the son of Alexandra Komnena Drakina (daughter of Theodora) would he include the name Drakos? His name should be Alexios Drakos-Di Lecce-Komnenos? (It wouldn't change anything for his son)
It's easy to see how the War of succession will go global... the order right now is:
1. Andreas Di Lecce-Komnenos Drakos;
2. Manfred Drakos- Von Wittelsbach (current King of the Romans, heir of the HRE, although his father is fighting a civil war with his uncle) and his brother Otto;
3. Andreas Drakos Laskaris (Heir of Russia) and his brothers Demetrios and Theodoros;
3. Demetrios Drakos Sideros (their mothers are twins) and his his sister Zoe Laskarina Drakina Sidera (married to the crown prince of EAN)[I don't include Anna Drakina Sidera, married to the Duke of Padua];
4. Gyorgis Solomon (Heir of Ethiopia) and his brother Quastantinos;
5. Miguel Drakos Trastamara (Son of the Crown Prince of Castille-Portugal);
6. Anna Drakina Bagrationi (Heiress of Georgia);
7. Bela Drakos Hunyadi (son of Crown Prince of Hungary);
And this is just considering Helena's descendants... If we were to include also Alexeia's and Theodora's (I think Theodora is older, but since she is adopted what would be the order between them?) you can add Arles, Prussia, Vlachia, Sicily again (Andreas' brother, Hektor).
If Andreas' main problem was that he sired too many children, the Triumvirate problem is the fact of who their children married (I guess it was kind of unavoidable once Venera Bagration died and Demetrios II didn't sire anyone else).
A small nitpick about the last update: The Megas Domestikos cannot be Anastasios Komnenos Drakos, who is the current King of Prussia, but Alexandros Komnenos Drakos, which is the uncle of:
- the Despot of Sicily, not Egypt through his sister Alexandra;
- the heir of Prussia, trough his brother Anastasios;
- the heir of Vlachia, though his sister Anastasia;
- the heir of Arles, through his wife Sophia Komnena;
So It's easy to see how the children of Theodora could make some noise given the fact that they could've on their side the Megas Domestikos.
His official full name is Andreas Doukas Laskaris di Lecce-Komnenos Drakos. For 'short' he's known as Andreas Komnenos Drakos.
Sicilian Despots don't count their time as Dukes of Abruzzi (new, superior title). When the Dukes of Normandy became Kings of England the regnal numbers restarted.
Despot Alexios does include the Drakos name as he inherits it from his mother but in contrast to his son he is Alexios Drakos di Lecce-Komnenos. His 'royal' family name is di Lecce-Komnenos so that comes last as the most important. In contrast his son Andreas has his 'imperial' family name as Drakos so that comes last.
Normally the last name inherited directly from the father would be the final one. For example Demetrios Sideros' full name is Demetrios Doukas Laskaris Komnenos Drakos Sideros. But since Andreas is direct heir to the Roman throne and Drakos is the Imperial dynastic name, in his case Drakos, despite being from the female line, takes precedence.
The Megas Domestikos is not Anastasios Komnenos Drakos, he's Anastasios Drakos Komnenos. The Despots of Egypt are descended from Vlad Dracula/Drakos (via his daughter Maria) and Demetrios Komnenos, eldest son of Andreas Niketas. Demetrios I of Egypt's children thus are styled Drakos (from Maria) Komnenos (from Demetrios-which was also the imperial and most prestigious name at the time).