I love living in the UK but I do wish people were better educated about the country right next door. Particularly its name.
The Constitution of Ireland sets out that there are two official names for the country, Ireland and Éire. Éire should only be used when speaking in the Irish language. Therefore it is correct for people in the UK to say Ireland when talking about that fab country next door!
Northern Ireland is a seperate place and is part of the UK.
Republic of Ireland is a description as opposed to a name. For political reasons FIFA forces the football team to use this name.
The term 'Southern Ireland' is very offensive and should not be used ever. It has strong historical connotations and was used by the English government as a way to avoid recognising the independence of Ireland. I understand that people genuinely do not know this and don't always mean to be offensive as so many people in England use it so casually.
I often see on here people referring to Irish accents and sayings as 'regional'. This is incorrect, Ireland is not a region of the UK no more than France or Spain are.