European Iberia is named after Ebro River in Spain, itself of Celt-Iberian origin (reconstructed *Ibēr). Caucasian Iberia was probably related to Old Armenian Վիրք 'Virk' referring to Georgians. More specifically Ancient Greek writers called Eastern Georgians Iberians, with the Western ones called Colchians (an exonym as well). Georgians call themselves ქართველები 'Kartvelebi'. So no, there is no relation. One is of Celtiberian origin, which is Indo-European, the other is from a Caucasian language.

We do not know what Caucasian Albanians called themselves, we only know what others called them. Old Armenians called them Աղուանք 'Ałuank', Parthians (Iranic people) called them 'Ardhan'. European Medieval Albanians were known as 'Arbëresh/Arbnesh' (depending on the dialect), reconstructed *albanensis, and the land where they lived 'Arbëria/Arbania), itself referring to a city in Central Albania recorded by Ptolemy as 'Albanopolis' and the people 'Albanoi'. The English names do not come directly from the native names of these people, so we know there is no connection here.

What we have here is misunderstanding caused by Hellenization and later Latinizations of native names. The English names come from Latin, the Latin names have Ancient Greek origin. But neither group has relation to the other.