Why is Leeds castle so named?

The name Leeds in 'Leeds Castle' derives from Old English hlyde (English {loud;} Dutch {luid;} German laut ). This was the name of a brook( 'the noisy one') near which a village (Hlydes= belonging or near to the noisy one) developed. Later the castle built near 'Hlydes' became Leeds Castle. The Domesday Book mentions an intermediate form of the village's name:'Esledes'.See Adrian Room's 'Dictionary of Placenames in the British Isles'.

Sorry but you are off track Flemish. Despite its name, Leeds Castle is nowhere near Leeds but is, in fact, near Maidstone in Kent, named after Led, Ethelbert IV's chief minister. It has been a stronghold, a royal home for six of England's medieval queens, one of Henry VIII's palaces and now it is a residence and corporate conference centre with an adjacent golf course.
http://stronghold.heavengames.com/history/cw/cw7

Some sites have different spellings of the name but agree that the castle is named after its first owner Led, Leed or Ledian who was the Chief Minister of the King of Kent. He constructed a wooden stronghold on the two small islands in a lake formed by the River Len.

Don't remember saying Leeds VILLAGE was at the origin of the TOWN of Leeds. Had heard of the link with some character of the name of Led. Only it does not seem to be confirmed by scholarly research.

I should know better especially as I live nearby, you are quite right Flemish that some of the well known tomes suggest that the name derives from the village nearby and that names derives from that of the brook on which it lies, in turn representing a conjectural Old English word hlyde (umlaut over the y) which means 'loud one'. Having been born in Kent and living a few miles from the Castle for over 27 years I can only say that I had possibly accepted one explanation as being the correct one and had thought that the village came later as it was quite common for villages to be built near castles.

You can find the village of Leeds mentioned in Ordnace Survey Map Landranger 188 Maidstone and the Weald of Kent. 1:50 000 map. South-East from Maidstone..
The etymology of Leeds in West-Yorkshire is quite different. The River Airze near Leeds was called the river Lat in medieval times. Lat is a word of Celtic origin and means flooding. Venerable Bede mentiobns Leeds as Loidis in eight century. The Yorkshire Leeds stands for: 'place of the people who live by the River Lat'. Same explanation can be given for Ledsham and Ledston near Leeds, Yorkshire.
As to Led..etc. I think the tourist brochure published for Leeds Castle does link the name to somebody of that name.
Seems to be a dispute between historians and linguists.
On the Internet I found no link to any other Mister Led than Led Zeppelin. But I
must admit a Led%3ELeeds explanation sounds attractive.

I am sure I heard about that 'Led-man' before. Thought they even spoke of a 'King Led'.Strangely enough the only tourist brochure I could check (published on behalf of the Leeds Castle {Foundation;1989)} gives a list of 'owners' of the castle in which no such 'Led' is mentioned.According to that source the holders of the Manor of Leeds were: 856-860 Ethelbert (under King of Kent). 1052-53 Earl Godwin. 1053-1066 Earl Lewin. 1066..of course William, aptly called the Conqueror.
In the chapter on the History of the Castle the author of the brochure says:' There is a LEGEND that the local thane of Esleds (Leeds) built a fort on the rocky outcrop in the valley of the River Len at this place, but of that no trace remains.'
Any chance that by that 'local thane' our 'Led' is meant?
Anyway whoever is at the origin of the manor, there is no doubt the manor is an absolute beauty.And for the old-fashioned pedestrian tourists among us: it's within walking-distance from youth-hostel at Kemsing via North Downs Way or Pilgrims' Way...

This webpage seems to agree with the castle being there before the village.

Leeds, a parish in the hundred of Eyehorne, lathe of Aylesford, county of Kent, 5 miles SE from Maidstone, containing 515 inhabitants... The church, dedicated to St. Nicholas, has at the west end a remarkably low square tower. Leeds is said to have derived its name from Ledian, counsellor to Ethelbert II., who built here a fortress in 978.

https://www.culpepperconnections.com/archives/uk/places/leeds.htm