So if the Vale is the Vale of Arryn,

[Angel Eyes]

How come the other Great Houses have their names alongside the names of their kingdom, i.e. the North of Stark, or the Reach of Gardener?

[Back door hodor]

Very interesting question....I don't believe we have a definitive answer but it could be because the vale seems to be the only time an andal family successfully became overlords of a large region of westeros and held the title. Thus a much larger and stronger pr campaign so to speak by the Arryns.

In every other region the ruling first man families managed to hold many lands and titles by intermarrying and allying with the invaders. At least in name. 

The north, dorne and the iron islands were also never fully andalized 

[Ralphis Baratheon]

Because Strong Robin is the last Arryn and anyone who tries to take the Vale from him will be cursed and fail ! 

[Springwatch]

Maybe the Arryn's named themselves after the Vale and not the other way around.

[Orphalesion]

7 hours ago, Angel Eyes said:

How come the other Great Houses have their names alongside the names of their kingdom, i.e. the North of Stark, or the Reach of Gardener?

Because that would sound ridiculously stupid?

More importantly, the North is not named "Stark" and neither is the Reach called "Gardener". Those places are called "The North" and "The Reach"
However with the Vale, the physical location, was named "Arryn" by the family, so it's not the name alongside the name of the Kingdom, "Vale of Arryn" IS the name of the Kingdom and would be so, no matter who ruled there.
From what I have read it also seems that not only was the Vale the first landing point of the Andals, but it's pretty much the place where their replacement of the First Men Population was the most complete (compare how many of the other great Andal houses are a continuation of the older First Men houses of the same name) so it's not difficult to picture the first Arryn king to take possession of the land and name it after himself.

Compare Washington D.C. Lousiana, Jamestown, Virginia, Adelaide, Charlotte and the various places called Victoria in the real world.

[Tygett Lannister]

8 hours ago, Angel Eyes said:

How come the other Great Houses have their names alongside the names of their kingdom, i.e. the North of Stark, or the Reach of Gardener?

Isn't Vale of Arryn only the valley in middle of entire Vale? Vale means valley so I guess they just named it "Vale of Arryn" which is same as "Valley of Arryn" "Valley ruled/owned by Arryns" ect. It might be Arryn's themselves calling it Vale of Arryn or more likely others (other nobles around the Vale of Arryn) started to call it that.

You can't really say Westerlands/Reach/North/Stormlands/Dorne of *houses* because Lannisters did't hold entire Westerlands, Reach don't really think has any geographical meaning, North wasn't entirely held by Starks ...

http://awoiaf.westeros.org/index.php/Vale_of_Arryn_(valley)

Quote

The Vale of Arryn or the Vale is one of the constituent regions of the Seven Kingdoms of Westeros. It was formerly a sovereign nation ruled by the Kings of Mountain and Vale before Aegon's Conquest. The Mountains of the Moon surround the smaller Vale proper,^[2] although the valley's name is often applied to all of House Arryn's realm.

 

[Melisandre's Rubies]

I'd say that part of it is what's being described. Most of the other areas are more geographical, where they are in relation to the realm and each other, eg. the north portion of Westeros, the west portion of Westeros, the area with many rivers, the lands around the king's base as the lands belonging to the Crown, etc. The Vale of is more a topographical description which would be more similar to The Wolf's Woods, The Wolf's Den, Casterly Rock, The Iron Islands (though in that case there seems to be more of the place determining the name Ironborn). It's distinguishing a particular feature, however, the Vale also has the Mountains of the Moon, The Fingers, Giant's Lance, etc. The Vale name was shortened from the Kingdoms of the Mountains and the Vale to the Vale of Arryn for all of the region. 

 

[Angel Eyes]

5 hours ago, Orphalesion said:

Because that would sound ridiculously stupid?

More importantly, the North is not named "Stark" and neither is the Reach called "Gardener". Those places are called "The North" and "The Reach"
However with the Vale, the physical location, was named "Arryn" by the family, so it's not the name alongside the name of the Kingdom, "Vale of Arryn" IS the name of the Kingdom and would be so, no matter who ruled there.
From what I have read it also seems that not only was the Vale the first landing point of the Andals, but it's pretty much the place where their replacement of the First Men Population was the most complete (compare how many of the other great Andal houses are a continuation of the older First Men houses of the same name) so it's not difficult to picture the first Arryn king to take possession of the land and name it after himself.

Compare Washington D.C. Lousiana, Jamestown, Virginia, Adelaide, Charlotte and the various places called Victoria in the real world.

It would sound stupid, but it’s still done.

[Dorian Martell's son]

14 hours ago, Angel Eyes said:

How come the other Great Houses have their names alongside the names of their kingdom, i.e. the North of Stark, or the Reach of Gardener?

The vale of Arryn sounds cool. The other places don't 

[ChuckPunch]

To me the more confusing thing is why "The North" doesn't have an actual name. Even "Westerlands" has a sort-of name to it instead of just The West. 

[Orphalesion]

6 hours ago, Angel Eyes said:

It would sound stupid, but it’s still done.

Where is it done? Do you have an example of an awkward, unnatural sounding and gramatically wrong construction such as "The North of Stark"?? In English and not just one that sounds good in in the language that's actually spoken there and is only awkward when translated.

[Angel Eyes]

2 hours ago, Orphalesion said:

Where is it done? Do you have an example of an awkward, unnatural sounding and gramatically wrong construction such as "The North of Stark"?? In English and not just one that sounds good in in the language that's actually spoken there and is only awkward when translated.

I guess I said it wrong. It’s stupid to say it, but the vale does it anyway.

[Ralphis Baratheon]

9 hours ago, ChuckPunch said:

To me the more confusing thing is why "The North" doesn't have an actual name. Even "Westerlands" has a sort-of name to it instead of just The West. 

The Northernerlands?

[Orphalesion]

10 hours ago, Angel Eyes said:

I guess I said it wrong. It’s stupid to say it, but the vale does it anyway.

Nope, the Vale doesn't do it. There is a physical place inside the kingdom called "The Vale of Arryn" and the name was adopted for the whole kingdom.
It's like "The State of Washington" So it's not "Region Name + Ruler Name" but only "Region Name"

You have to look how these names would work:

'The Vale of Arryn" implies that there's a valley called Arryn. Vales/Valleys have been designated like that before in the real world and in fiction.Vale of Glamorgan
""The North of Stark" meanwhile implies hat there's a place called "Stark" and you are talking about the northern portion of that place called "Stark"

[Angel Eyes]

3 hours ago, Orphalesion said:

Nope, the Vale doesn't do it. There is a physical place inside the kingdom called "The Vale of Arryn" and the name was adopted for the whole kingdom.
It's like "The State of Washington" So it's not "Region Name + Ruler Name" but only "Region Name"

You have to look how these names would work:

'The Vale of Arryn" implies that there's a valley called Arryn. Vales/Valleys have been designated like that before in the real world and in fiction.Vale of Glamorgan
""The North of Stark" meanwhile implies hat there's a place called "Stark" and you are talking about the northern portion of that place called "Stark"

Ok, I think I get it.