Wind storms in Europe are really only named in some countries (UK, Ireland) - take 'ex-Ophelia' for example.
bad example. While it was part of the windstorm season, it wasn't named in it as it had already been named and they decided not to rename it 'Brian'.
Norway called Desmond 'Synne'. Angus was 'Nannette' in France, Belgium, Netherlands and Germany. 'Some countries' seems to be most of them that get Atlantic weather! Denmark and Sweden also name storms that are relevant to them. France, Spain and Portugal announced co-ordinated systematic names at the beginning of last month and have had Ana, Bruno and Carmen.
I gather the UK & Ireland and Franco-Iberian names list will be co-ordinated so as to be the same next season. At least that will mean less chance of having to pronounce Gaelic names (it's phonetic, but with different sounds to English). I'd imagine that the Dutch, Danes, Deutsch, etc will want in too and will have one Europe-wide system for naming North Atlantic extra-tropical cyclones.
The Met Office in the UK names winter storms.
Not quite. The Met Office, along with Met Éireann, name winter storms.
We had Eleanor (very English name - even though it's Greek via Provençal) earlier this week, and the next one will be Fionn (very Irish name that English people can't pronounce properly - I gather it's Fy-unn).