I use the shorthand "NI" or "ROI", because it's, er, the shortest. And "Northern Ireland" and "Republic of Ireland" are also the official team names, as determined by FIFA, the governing body in such matters, over 50 years ago. Which is why the IFA and FAI themselves use those terms e.g. on their website and in their programme etc.
And as for fans using the term "Ireland" in everyday use, of course that will happen and there's nothing sinister about it. However, of the two Irish teams, the IFA unquestionably has the prior "right" to do so, since we were the original "Irish Football Association". Which is why FIFA permitted the IFA to continue to use the designation "Ireland" for British Championship matches, a situation which pertained until the IFA dropped it voluntarily (around 1970?). Which is why, btw, I recall chants of "C'mon Ireland" etc at Windsor even after that date.
"And if - you know - your History..." ;)