I have no idea about genetic or blood relations, but modern Macedonians are cultural descendants of Slavic settlers which came into this province during late 6th and 7th century. Connection to ancient Macedonia is on pretty shaky ground.

I can give quick overview of naming dispute. After the conquest of Kingdom of Macedonia in 146 BC, Romans established province of Macedonia, during Roman era province often changed its boundaries but at times included whole or parts what we now know as FYROM (Former Yugoslavian Republic of Macedonia). During the Byzantine era there was Theme of Macedonia, it was centered around Thessalonica, though at times it included parts of modern FYROM, but its borders mostly corresponded to modern greek province of Macedonia. See for example famous Byzantine dynasty of Macedonians, which had its origins in Theme of Macedonia.

During late medieval and with Ottoman conquest geographical term fell out of the usage, and whole are was administered by turkish eyalet of Rum.

The name Macedonia as termn was revived by group of Bulgarophiles who operated in the are of modern FYROM. Their goal was to educate and organize Slavic people in region. It was quite common for South Slavs revive ancient Roman terms. For example Croatian cultural movement in 19th took name Illyrian as means to unite different ethnic groups. The name caught on, and started to be name for region and people. In 1944 local communists called the new republic of Yugoslavia Democratic Macedonia and since then the name was codified for both people and the state.

George Ostrogorsky, History of the Byzantine State (1957.) Misha Glenny, The Balkans: Nationalism, War and the Great Powers, 1804-1999 (1999.)