I think it depends on what questions you’re asking and how you want to define things.
If you’re asking “would people find it inappropriate if I use an Irish name when I have Irish ancestry but no personal connection to the country?”, you’re basically asking “am I Irish enough to use the name?”.
In that case it would be good to find out what Irish people think make you “Irish enough” and I’ve found that Europeans generally don’t use percentages for but rather which culture/s you grew up in.
I think the way it’s mostly viewed here is more along the lines of your ancestry/blood gives you a gateway/reason to learn about a certain culture, visit the country, learn the language, celebrate their traditions and perhaps become part of it eventually; it doesn’t automatically make you Irish/German/Italian/etc.
However, as we both said, it really doesn’t matter for 99% of the cases, especially not in Europe.