Name Search Continued

So far, in the various sources I've been finding, I can't actually find a reference for when "Ireland" became Ireland. Granted, "Ireland" is the English translation of Eire, but when did they first call themselves Eire? Okay, that I can find thus far, Ireland has been called the following Erinn, Eire, Eriu (after a goddess), and Hibernia. Hibernia is what Ptolemy, a Greek who lived in the Hellenistic culture of Roman Egypt, called Ireland in 100 AD (Ptolemy's Geography). Therefore, until I find something that tells me otherwise, I think I can safely continue the thought that Ireland has simply been Ireland throughout the medieval period, even unto the first years.