Why isn't the county called Lancastershire?

For long after the Romans had left Britain, the north-western part of this country was to all intents and purposes a waste. In the "Domesday Book" itself there is no mention of Lancashire. All the land between the Ribble and the Mersey is in that book included in Cheshire, and the land to the north of the Ribble in Yorkshire. Just when the county of Lancashire, in the shape we know it today, came into existence it is difficult to determine. Though the Pipe Rolls of 1168 refer to a county of Lancaster, that indicated merely the north of present Lancashire. True, the rest had broken away from Cheshire, but it had become a separate territorial division, "'twixt Ribble and Mersey." When the fusion did take place, "Lancastershire" and not "Lancashire" was the first title and, in the time of Henry Viii, Leland, the antiquarian, was still using it.

http://www.british-towns.net/england/northern/lancashire

The County isn't called Lancastershire because its name is Aroostook.

Aroostook County (known as the County) is a county located in the U.S. state of Maine. In 2000, its population was 73,938. It is the largest county in the state. Its seat is Houlton. In land area, Aroostook County is the largest U.S. county east of the Mississippi River. Among residents of Maine, it is often referred to simply as "the County."
https://en.wikipedia.org/wiki/Aroostook_County,_Maine

Aroostook was named for its most prominent river, and is derived from a native Wabanaki word, sometimes spelled Restook, Ristook, Aroostic, and finally, Aroostook.

Different people have assigned different meanings to the name in the original language. Moses Greenleaf supposed that it is the same name as Wal-loos-took, the Wabanaki name for the St. John, which he understood to mean good river or fine river. On the original tracing of the map that he drew of Maine, drawn about 1814, it was spelled in the way that it is now spelled -- Aroostook.

Sockabasin, a Penobscot Indian, told William Willis in 1840 that the name meant smooth river. In his Woods and Lakes of Maine, L. L. Hubbard writes: "Aroostook, Alloostook, Oolastook, 'beautiful river'," and refers to Rand's Micmac Reader. Wallastook, or Woolastook, he says, means "stream where you get smooth boughs." He concludes that authorities generally think that the word means fine, good or beautiful river.
http://kenanderson.net/aroostook/war.html

My question was perhaps not clear. Most British counties get their name from the main city in the region. So you have York, and the area around it is called Yorkshire. Shire means county. So we have Oxford in Oxfordshire, Cambridge in Cambridgeshire, Aberdeen in Aberdeenshire, etc. So why is the county called Lancashire, not Lancastershire as Lancaster is its historic capital?

It's called syncopation.

In grammar, syncopation means to eliminate sounds or syllables out of the middle of a word, as opposed to abbreviation, to leave things off the back, or clipping, off the front. A lot of well-known British proper names are syncopated in pronunciation, spelling, or both. Austin is English for Augustine. Bedlam is from Bethlehem — the hospital of St. Mary of Bethlehem was the London insane asylum, where they used to sell tickets so the lunatics outside could watch the ones inside. Covent Garden started life as "Convent", and Worcester is pronounced "Wooster". Cheshire and Lancashire are "Chestershire" and "Lancastershire", from their chief cities, and Londonderry is pronounced "Londonry".
[ io.com/~dierdorf/ww-21.html no longer exists ]

https://www.prismnet.com/~dierdorf/ww-24.html

Brighton was abbreviated from Brighthelmstone. Wraysbury- Wyrardisbury. Arbroath- Aberbrothock etc. Many longer names in Britain were shortened for convenience but some like Aberbrothock remain the official name as does the Wyrardisbury River which was not abbreviated, while the parish retains the long name as well. I am assuming Cheshire and Lancashire where shortened for the same reason.

https://en.wikipedia.org/wiki/Arbroath
https://en.wikipedia.org/wiki/Brighton