What is the longest country name, and the longest county name?

The United Kingdom of Great Britain and Northern Ireland - 48 characters

It can be considered a country:

Although the United Kingdom, as a sovereign state, is a country, England, Scotland, Wales, and to a lesser degree, Northern Ireland, are also regarded as countries, though they are not sovereign states.

Yes, that is its official name:

The full title of this country is 'the United Kingdom of Great Britain and Northern Ireland'. Great Britain is made up of England, Scotland and Wales. The United Kingdom (UK) is made up of England, Scotland, Wales and Northern Ireland. 'Britain' is used informally, usually meaning the United Kingdom.

https://en.wikipedia.org/wiki/United_Kingdom

The Former Yugoslav Republic of Macedonia 36

Saint Vincent and the Grenadines 28

Democratic Republic of the Congo 28

Federated States of Micronesia 27

People's Republic of China 22

United States of America 21

Bosnia and Herzegovina 20

The United Kingdom of Great Britain and Northern Ireland 48

Thailand boasts the world's longest name: Krung-thep-maha-nakorn-boworn-ratana-kosin-mahintar-ayudhya-amaha-dilok-pop-nopa-ratana-rajthani-burirom-udom-rajniwes-mahasat-arn-amorn-pimarn-avatar-satit-sakattiya-visanukam.

We sought a ruling from a Bangkok wordsmith, Theppitak Karoonboonyanan, who said the correct spelling (163 letters) is: Krungthepmahanakornamornratanakosinmahintarayuttha
yamahadilokphopnopparatrajathaniburiromudomrajaniw
esmahasatharnamornphimarnavatarnsathitsakkattiyavi
sanukamprasit.

http://www.fun-with-words.com/longest_place_names.html

Cambridgeshire and Isle of Ely (England) has 26 letters - this is the longest in all of the UK and Ireland.

https://en.wikipedia.org/wiki/List_of_counties_of_the_United_Kingdom

Longest in USA is 14 letters.

The award for longest county name (14 letters) is a tie between Northumberland County, Pennsylvania and Northumberland County, Virginia.

If we're allowing non-English names:

Al Jumahiriyah al Arabiyah al Libiyah ash Shabiyah al Ishtirakiyah al Uzma also known as Libya is the world's longest country name at 74 characters with spaces and 63 characters without.