the word for shrubbery that grows on a house

There is. It's called ivy.

Creeper, maybe?

Ivy is one, but there are others like grapes, for instance. Of course, maybe the specific word is better any way.

"Ni!"

or

"Ekke Ekke Ekke Ekke Ptangya Ziiinnggggggg Ni!"

(Sorry, I see "shrubbery" and can't help myself."

There are lots of ivies.
Some grow into the wood/stone/structure via aerial roots or suckers; some grow on trellises(sometimes they have to be tied to the trellis), which can be attached to the structure or free standing.
Ivies can be destructive.
In general, watch out for the wisteria; it is not only fast, it's determined.

Perhaps Roger The Shrubber will know...

Cyia said:

"Ni!"

or

"Ekke Ekke Ekke Ekke Ptangya Ziiinnggggggg Ni!"

(Sorry, I see "shrubbery" and can't help myself."

Click to expand...

oh don't get me started...

"One day, my son, this'll all be yours."
"What? The curtains?"

Well, they're all vines, but one that takes over my house is the trumpet vine. I swear it grows as fast as the green stuff in Jumanji. They stick to bricks, work their way between the roof and eavestroughs and bite into the window screens.

If they weren't so invasive, I'd let them run rampant. the hummingbirds love the vermillion flowers.

If...

you don't know what it is then it's called a creeper or creeping vine in the UK/Commonwealth as in:

The house was covered in some sort of creeper /creeping vine.

If you're looking for a specific plant, "Virginia creeper" and "Boston ivy" are two common ones that turn scarlet in autumn. Ivy is evergreen.

Just don't go calling it a "verdant mantle".

The estate agents are fond at describing it in terms of cladding: an ivy- clad cottage, the walls have a cladding of wisteria, etc.

Generally, I suppose they are just referred to as climbing plants.

Ivy is a specific family of plant that happens to climb/creep.

"Creeping" or "Climbing" plants are a wider variety of plants that will either spread across the ground or climb up something. Strawberries are an example of creeping plants. Grapes are an example of climbers.

Many buildings are described as "ivy covered" because that's what they are, as ivy is the usual suspect for this type of thing.

Just go with what sounds best, or Google descriptions of stogy private universities and see how they describe the ambiance of their institutions.