What is the official name of Scotland?

It's simply called Scotland although in Gaelic it is known as Alba (pronounced All-a-pa). Ptolemy spells it as Alouion around 127 AD, and later on Pliny refers to the island as Albion.

The Greek seafarer Pytheas, who as early as 300 BC refers to the islands Pretanikai Nesoi (meaning "Pretanic Islands"), which at least one authority claims was based on the native name for Britain Ynis Prydain, which literally means Picts' Island. Another scholar derives the name "Pritanic" from the Pictish tribe called Pritani, meaning "The People of the Designs."

The Annals of Ulster refer to Scotland as Cruithintuait - the word Cruithni (meaning "the tribe of the designs") being the Irish word for the Picts and tuath for people, land or nation. This ties in with the myth of an early king of the Picts, Cruithne.

It was also known as Caledonia - derived from Caledonii, the Roman name of a tribe in the northern part Great Britain or what is now Scotland.

After the union of the crowns of England and Scotland on the accession of James I & VI in 1603 and the subsequent union of the parliaments in 1707, for a time Scotland was 'rebranded' as North Britain, but such was the unpopularity, especially and particularly amongst Scots, that it remains Scotland.

Until the union with England in 1707 Scotland was officially known as the Kingdom of Scotland (see the link below).