I understand this is a very narrow topic and we probably don't have many specialists in this field here, but I'll try my luck.
One of the most famous Dukes of the Grand Duchy of Lithuania is currently known as Vytautas. This is the name used in Lithuania, also the name English wikipedia uses as the "main" name and the title for the article. Russian Wikipedia gives us Витовт which is basically Russian form of the same Vytautas written in Cyrillic. Wikipedia articles in many other different languages use some form of Vytautas as well, but none provide any sources so I assume they just use the currently popular name.
However as far as I know this is a made up name. Lithuanian linguist Kazimieras Būga made it up at some point in late 19th or early 20th century. While Lithuanian sources say he just "restored true names for Lithuanian dukes" they never provide any evidence for it. I don't even know a rationale behind his decision, i.e. why Vytautas and not Vitoldas, what made him think this is a "true" form of the Duke's name. And since the times Būga lived in are known as rising nationalism times for Lithuania, and Vytautas just happened to be similar to tauta (Lithuanian for a nation), it makes me even more suspicious this name is just a made up name with no real roots in history.
So my question is, how much do we really know about the real name of Vytautas and all other dukes from the Grand Duchy of Lithuania? Since many of them were "restored" by Būga, including but not limited to Vytautas' father Kęstutis, the King of Lithuania Mindaugas and so on. I know the Latin name for Vytautas was Alexander Vitoldus, is it possible that Vitoldus was his real name? Or is it more likely it was just a latinized form of his real name that nobody knows now?
It's likely that his name was something like Vytautas--certainly close enough that it makes no difference. Forms like Vitoldus are probably misreadings of the name as it was written in Polish sources.
To understand why we can be fairly sure Vytautas was named Vytautas, we need only a basic knowledge of the historical phonology of Slavic. The name is attested in Polish first, I am fairly certain, as Witołd; in Old East Slavic as Vitovtъ. We know that in Polish, Common Slavic *l changed or was changing to /w/ (the value of the letter ł in Modern Polish). At least in Muscovy, the letter v had the value of /w/ into the fifteenth century. So, the lvu alternation is accounted for quite easily. The ao alternation is similarly explainable: in Proto-Balto-Slavic, long and short *o and *a merged to a vowel with a single quality (though still distinct in length). In Slavic, the short *a/o became /o/, and the long one became /a/. In Baltic, they both turned out as /a/. This takes care of the oa alternation.
It was common practice when Slavic speakers adapted male names from Latin or Greek to substitute native endings for the -us or -es, so you have (Russian) Mark Antonij, Tullij (analogous to English Tully, now outdated), Plinij (again, see Pliny for a parallel), Sokrat, etc. When the names were first adapted into Slavic, people were aware of the grammatical status of these endings, and substituted native Slavic endings in as appropriate. The same process clearly happened with Vytautas, and in fact the -as of Lithuanian is exactly cognate with the zero ending you find in modern Polish and Russian and the -us you find in Latin.
This sort of knowledge is where you get the Lithuanian forms, about which we can be fairly confident.