Ok, I will try to explain this in detail:
I'm sorry, but what you said is not enterely correct.
I am Galician, and I can confirm as someone who has studied history and collaborated with the Royal Galician Academy on the past, that the name of Galicia is a historical evolution of the name that the Romans gived to those lands: Gallaecia.
The name of Galiza, was a term used for 200 years at the colloquial level, but never was official, only was a vulgarism, used by people when they spoke on ambients not formal.
At that time, the official name was Gallizia, in fact, it can be see that, Alfonso X The Wise, in one of his letters of 1313, mentioned the name of Gallizia, as a derivative of Gallaecia, this being a missing link in history, a term intermediate between word Latin and the final term: Galicia.
However, it is true that the term Galiza, was a term that at a colloquial level had a period of use between the XIII and the XV, since the constant interaction with Portugal had its effects, becouse on portuguese to Galicia, it's called: Galiza .
However, one can speak of the Kingdom of Galicia as early as the 11th century, that is, 2 centuries before the colloquialism of Galiza existed.
At that time: Kingdom of Gallizia.
However, all this information is superfluous, if we consider that currently, this term was recovered of the past, (After a long time without use it), only for political purpouses of a bit group of radical reintegrationists, whose represent a minority of this region and only search to generate hate and fracture on the society.
Making an analogy, the swastika symbol was a symbol that represented well-being on multiple cultures of the past, but after the passage of the Nazis for the West, here it has become a symbol of Nazism.
Well, in Galicia, the term Galiza has become a symbol of the reintegrationists and their movement, dispite off its origin totally humble. The truth is that today, it has been transform to be a symbol of ideological thought of a politician movement.
That's the problem.
In fact, although the name Galiza would had been official at some point in history, currently it is not, so it should have the current and official name. Or is someone still calling Russia, The Urss?
I wait that now, you can understand me absolutely. I was trying explain this clearly. ¿^.^
By the way, I recommend you visit Galicia one time on the life, it's really probably that you want repeat.

^.^
Best regards, and thanks for your patience and time.