This is an incredible simplistic post on a very complex issue
By law, and as voted by referendum in Northern Ireland with the Good Friday agreement, people born in Northern Ireland are entitled to citizenship of both countries
All sports bar football are played on all-island basis. Hockey and rugby in Northern Ireland are predominantly played by people who would call themselves British and the national associations there use a compromise flag and anthem to appease them (not in a patronising way, they actively wanted to encourage inclusion). Hockey is an interesting case as Ireland could not even enter Olympic qualifying until 1992 as the Ulster branch of Hockey Ireland objected to it as they wished to align themselves with GB for Olympic purposes (with several winning gold in 1988).
This doesn’t apply at the Olympics. Obviously for individuals it is easier for them to choose federations
As there is no physical border, the nearest club/training facility for athletes living near the border may be on the other side of that borderline. Your line about it being known but not publicised is odd because thousands do it for work reasons and no one cares. As mentioned above Rhys McClenaghan won gold in gymnastics at the commonwealth games and he lives and trains in Dublin at the Irish national sports centre (and lives in Bangor, NI when not training).
To summarise, people born in Northern Ireland are free to choose British or Irish citizenship and individual athletes from NI are free to represent GBR or IRL in international competition
Many others will have family ties in either country (particularly as Ireland has a long history of emigration to GB) and athletes born in either country but with parents or grandparents from the other can represent them
The wider issue of why someone from NI would choose to represent one over the other is a different, more complex issue and one that I’m afraid you’ll have to research yourself