Can anybody give me a single word for a secluded garden surrounded by a wall?
It's actually called "walled garden"
A walled garden is specifically a garden enclosed by high walls for horticultural rather than security purposes, though traditionally all gardens have been hedged about or walled for protection from animal or human intruders. Garden walls may also serve a decorative purpose, but their essential function in the north temperate zone has been to shelter the garden from wind and frost.
Curiously, the literal meaning of the word "paradise" IS "walled garden" but it has long since lost that meaning
The word "paradise" entered English from the French paradis, inherited from the Latin paradisus, from Greek parádeisos (παράδεισος), and ultimately from an Old Iranian root, attested in Avestan as pairi.daêza-. The literal meaning of this Eastern Old Iranian language word is "walled (enclosure)",from pairi- "around" + -diz "to create, make". The word is not attested in other Old Iranian languages (these may however be hypothetically reconstructed, for example as Old Persian *paridayda-).
Maybe you can also use hortus conclosus
Hortus conclusus is a Latin term, meaning literally "enclosed garden". "The word 'garden' is at root the same as the word 'yard'. It means an enclosure", observed Derek Clifford, at the outset of a series of essays on garden design, in which he skirted the conventions of the hortus conclusus.1 Thus, at their root, both of the words in hortus conclusus refer linguistically to enclosure.
Pleasance seems to fit the bill quite nicely. -- ODO
(noun) A secluded enclosure or part of a garden, especially one attached to a large house.
Courtyard -- Dictionary.com
(noun) a court open to the sky, especially one enclosed on all four sides.
What came to mind are the ancient Roman homes where the second half of the house is surrounded by a peristyle. The use of the word peristyle would be specific to a colonnade with a covered walkway and may not always contain a garden. However, I have seen peristyle garden and peristyle courtyard as alternatives. There is also a cloister, the medieval equivalent.
Secret garden is another possibility.
Bower comes to mind. -- ODO
(noun) 1. A pleasant shady place under trees or climbing plants in a garden or wood.
Perhaps you could try plantiecrub, although this source here suggests it would be for growing cabbage.
noun - a small circular dry-stone enclosure for growing cabbage plants.