This is horrifically complex and controversial, I'll refer you to the Wikipedia page on the terminology with a health warning - it starts getting complex in the 4th c. BC when Alexander's the Great's Kingdom falls apart after his demise and it doesn't ever get simple.

There is not a single modern day Macedonia - instead there are several areas, including most notably the modern Republic of Macedonia and the region of Macedonia in Northern Greece which claim the right to use the name. They have heated diplomatic disputes over this issue.

The main thing to be aware of in the modern context -

The Greek government wants you to call the Republic of Macedonia 'The former Yugoslav Republic of Macedonia' the Republic of Macedonia considers this about as insulting as calling Greece 'the former Ottoman colony of Greece' and wants you to call them just 'Macedonia' or 'the Republic of Macedonia' so far the Greek government has retained the upper hand and in official international contexts such as the UN and Soccer tournaments they are known as FYROM. But if you meet a Macedonian from the Republic you're best off just calling them 'Macedonian'