There is a Sanskrit rule called "Samprassana" or making of Vowels into Consonants, where "u" becomes "v", "i" becomes "y", and "R(i)" becomes "ar".
So "uttar" is a comparative pronoun and it becomes "vattar" which becomes "better".
"b" and "v" are two sounds that get intermixed.
Like a Bengali Indian would say "Bijoy" instead of "Vijay" (note "a" becomes "o" also).
Same way the state of Bihar was actually called Vihar during its golden period, literally meaning Paradise (another word taken from Sanskrit and Persian, and is actually "para-desh", the state beyond, which is heaven).
Now it is another matter that it has become a "Bekar" State (useless), but still produces many Intellectuals but most of them chose to go to IAS (Indian Administrative Services) only to become corrupt Beauracrats.
Or "Varma" becomes "Burma" or "Varman" becomes "Burman". "Varman" is the generic noun root which means "chosen one" or "the best", e.g., because you choose the best. "Varma" is Singular Subject Noun.
Yes that brings to "Uttar Pradesh" which has become "Ulta Pradesh" (the upside down State).