I would disagree with this. Many French, Spanish, Greek, German and the like make sense in English at least to some extent because they are all of similar origin. English has many french-origin words, is Germanic in nature and took many words from Greek and the Romance languages. Irish however is completely different. It is of the Indo-European tree, but it is not really as tied into the other languages as some Indo-European languages are, and is completely foreign to English Speakers for the msot part.
Many irish names have an anglacized version for a reason, to make them more user-friendly to people who do not speak or understand the native tongue. I am not saying it is wrong to use them, just saying that they are a bit different than French, German, Spanish, etc. names for English.