The two countries Greece and the Republic of North Macedonia had a conflict since the second country declared its independence under the name of Macedonia in 1991. The core of the dispute is about the name of one of the successor states of the former Yugoslavia because there is a confusion between the name of the country and the historic region of the neighboring country, Greece which has the same name.
The Republic of North Macedonia became a member of the United Nations (UN) in 1993, but it was admitted under the notion: the former Yugoslav Republic of Macedonia. 

The Mediator

In this case, the mediator Matthew Nimetz is jewish born in America. It must be taken into consideration that traditionally the jewish population was numerous in both countries until the Nazi Germany’s occupation started, which might cause a bias for a jewish person, when it comes to trying to make peace and acceptance of other nations in these countries. 
A UN mediator is the right choice since he is not only neutral but is also very motivated to make peace between two members of his organization to eliminate any possible inner tension. Although his origin might implicate that as an American it is not his interest to push for peace and cooperation between the parties because the weaker other countries are the stronger the United States looks, but at the same time the United States needs strong trading partners to boost its economy. That means that his goal is to stabilize the relations in the European Union. It might also seem to be a bias to work for the goals of an organization and not just be a neutral guide through a conflict, but in a way leading towards peace always means a bias towards the solution that is peaceful no matter which party agrees with it more.

Why the UN?

Based on the nature of mediation a third party is needed to help the parties reach an agreement. In this situation, a third party may be another country or an international organization which either includes both of the countries or non- of the countries. There hasn’t been a third sovereign country that applied and was then accepted to the role of mediator. The reason for such few interest might be that the two countries are not on the verge of physical conflict or taking any action that might be against the interest of other countries. It means an international organization had to take on the role. The UN is behind both countries although in this specific case there is some asymmetry. The UN and other international organizations such as the North American Treaty Organization (which has a strong group of countries supporting Greece in this situation) that had been calling the Republic of North Macedonia the former Yugoslav Republic of Macedonia, (which wasn’t its official name) simply for the reason of acceptance from Greece, for about 27 years. It means that the UN has already stated in its own way that the name “Macedonia” will not be suitable for the country on the long run. This sheds light on the aspect of a scenario where the mediator might be unbiased as a person but the sending organization gives him a biased agenda to execute.

Other perspectives

Bulgaria doesn’t support certain compromises that include a name referring to northern territories that would suggest Bulgarian territories as well. It means Bulgaria stands with Greece, because it discourages any name change that might contain geographical elements that, hints at Bulgaria. It also suggests that the Macedonian-Greece conflict maybe wasn’t simply a naming dispute but it was meant to be a territorial dispute which they didn’t want to decide in the old-fashioned way by weapons, but in a diplomatic way.
The postponing of any solution may be the interest of any country that has an invested interest in weakening the EU, like Russia. It means Russia supports the Republic of North Macedonia to keep its ‘original name’: Macedonia. Russia has an interest in having good economic relations with countries in the Balkan.
This sheds light on one more hidden conflict at the core of the actual conflict. History had seen puppet states of two giant states in conflict, the US and today’s Russia. The Macedonia-Greece conflict might just be another one of those smaller battles in one big war.
On 17 June 2018, the Republic of North Macedonia and Greece signed the Prespa agreement. Macedonia officially changed its name to “Republic of North Macedonia” and it has a national referendum pending on the matter and legislation passing through parliament.

In my personal opinion in such cases the mediators of the United Nations organization are in the most optimal position to lead two parties in conflict to an understanding. The purpose of the United Nations by nature is to make members sit at the same table and work together which is the exact same action that a mediator wishes to do when working with parties in dispute.

References:

1, United Nations webpage (http://www.un.org/en/member-states/)
2, https://en.wikipedia.org/wiki/Matthew_Nimetz
3, https://www.rferl.org/a/greece-macedonia-name-dispute-nimetz-un-talks/29004400.html
4, http://greece.greekreporter.com/2018/02/16/bulgaria-issues-warning-over-macedonia-name-dispute/
5, Sarantis Michalopoulos: Bulgaria’s EU Presidency sees an ’opportunity’ in Sofia on Macedonian nam dispute, May 15, 2018 (https://www.euractiv.com/section/enlargement/news/bulgarias-eu-presidency-sees-an-opportunity-in-sofia-on-macedonian-name-dispute/)
6, John Smith: Bulgaria Issues Warning Over ‘Macedonia’ Name Dispute, February 16, 2018 (http://greece.greekreporter.com/2018/02/16/bulgaria-issues-warning-over-macedonia-name-dispute/)
7, Helena Smith: Macedonia agrees to new name after 27-year dispute with Greece, June 12, 2018 (https://www.theguardian.com/world/2018/jun/12/macedonia-agrees-to-new-name-after-27-year-dispute-with-greece)