As everybody knows the Galicians controlled ALL of the North Coast and most of the West Coast of the Iberian peninsula. Celt-Iberians controlled the interior. A variety of other people controlled other sites, and depending on the ebb and flow of fortune and disease, different regions dominated at different times.
However, the use of the word "Spain" is an affectation in the English language that allows us to refer to what is quite clearly a socio-political region as well as a geographical expression.
You can call it Iberia or whatever you wish, but we all know where it's at.
And no, the Visigothic Kingdoms weren't really serious entitites ~ Galicia, though was, as were the three states founded by King San Cho Noe I ~ Castile, Leon and Carvajal.
Together, through time, those three states wrested "Spain" from the hands of the Moors and others, and all of that was done without the assistance of the English.