The Galicia in Spain comes from the Roman province C/Gallaecia, which was named for a Celtic tribe, C/Galleaci that lived in the area. In Eastern Europe, Galicia comes from a latinized form of the city Halych (became popular after Hungarians conquered the area in the 1200s).

I don't know the other one off hand. Iberia (Spain/Portugal) comes from the Greek term for the Ebro river, (H)Iberus, because the Ebro was (partially) used to differentiate Iberia and Gaul (along with other physical features like the Pyrenees). After searching for a bit, I couldn't find a definitive etymology for the Caucasian Iberia. One hypothesis I found derives the name from Armenian designations for Georgians. Another one derives it from the Colchi (a contemporaneous Caucasian region) word "Imer" meaning "country on the other side of the mountain" because a mountain range separated Colchi and Iberia.

In all, in both cases, it is most likely a coincidence that the regions have the same names.

The Caucasian Iberia and Albania is kind of unknown, though there are theories. Donald Rayfield wrote in Edge of Empires: A History of Georgia that (to paraphrase) Iberia comes from the Phoenician 'ebr, meaning "over there", and in antiquity parallels were used (which is why Iberia and Albania are both on extreme east and west; Albania being the extreme west of the Balkans, of course). He also notes that Iberia also likely come from the Speri people of the northeast Anatolia (which as noted in another post, the Armenian term for Georgians, ivirk, also has the same etymology). I will note though that Rayfield doesn't provide a source for this claim (the entire book lacks significant notation, which is one of my major issues with it), but he is a reputable historian of Georgia, so take that for what it's worth.