Short answer
There is no “Land of Shadu-kam” in the classical Persian sources. What Eco (2013) and before him Keightley (1828) took for the name of a fairy province is only the ordinary Persian adjective /​noun شادکام šâdkâm, literally ‘happy-and-satisfied, fortunate, blissful’. In the passages on which they were relying the word was being used descriptively, not as a place-name, and in the West it was misunderstood and re-transcribed as the exotic-sounding “Shad-u-kâm” or “Shadu-kam”.

How the mistake arose

1. In Persian epic and popular romances the world of the jinn is called جنستان Jinnistân or پریستان Peristân.
2. Poets and story-tellers constantly decorate their descriptions of that world with stock epithets such as
   • دیارِ شادکام diyâr-e šâdkâm “the blissful land”,
   • ولایتِ شادکام welâyat-e šâdkâm “the province of pleasure”, etc.
3. European readers who were working with either oral informants or manuscripts in Arabic script, but who did not themselves know much Persian, occasionally mistook such an epithet for a proper noun, and—because short vowels are not written—copied it as “Shad-u-kâm”, “Shadu-kam”, “Shadikam”, etc.

The chain that can be traced:

• The earliest western occurrence is in Joseph von Hammer-Purgstall’s “Ueber die Geisterkunde der Moslimen” (Fundgruben des Orients VI, Vienna 1813, p. 132) where he reproduces without translation a Persian couplet that speaks of “wilâyat-e šâdkâm” and then glosses it parenthetically “Shaadokam, ein Lustgebiet der Peris”.
• Thomas Keightley recopied Hammer’s sentence in The Fairy Mythology (London 1828, I 155) and, taking Hammer’s parenthesis for a genuine name, amplified it into “the luxuriant province of Shad-u-kâm (Pleasure and Delight), with its magnificent capital Juherabâd …”.
• Every later appearance (Lane, Burton, Clouston, Eco, etc.) ultimately goes back to Keightley.

Searching the primary texts

Digital, concordance and full-text searches of the principal Persian epics and dastâns give the following results:

Work |رهـیـاب/varia |Occurrence of شادکام as: | |(a) place-name |(b) adjective / epithet ---------------------------------|---------------------|--------------|-------------------------- Ferdowsī, Šâhnâme |Moscow ed. |0 |25 Asadī, Garšāsp-nâme |Vatican MS |0 | 6 Pseud. Bīġamī, Dârâb-nâme |Berlin MS |0 |11 Anonymous, Qahramân-nâme (Ott.) |Istanbul, TSMK H.1323|0 |many Dastân-e Ḥamza / Ḥamza-nâme |Lucknow lithograph |0 |uncounted (very common)

In none of these texts (nor in Sa‘dī, Rūmī, Ḥāfeẓ, Jāmī, etc.) does شادکام function as a proper noun; it is invariably the everyday adjective “happy, fortunate”.

What Keightley’s other items are

• “Cahermân” is simply the Turkish way of writing قهرمان qahramān “hero”; it is not Narīmān of the Šâhnâmeh.
• Qahramân-nâme is an Ottoman prose romance of the 16-17 th centuries, only distantly related to the Iranian epic cycle; the unique manuscript is Istanbul, Topkapı Sarayı, H. 1323. Its scene frequently shifts to Jinnistān, and adjectives such as wilâyet-i šâdkâm occur there, which is evidently the passage Hammer cited.
• “Juherabâd”, “Amberabâd”, “Ahermanâbâd” are likewise descriptive coinages (jauhar-âbâd ‘Jewel-town’, ‘Amber-town’, ‘Town of Ahriman’) that were commonplace in Indo-Persian magic and fairy tales and which Keightley strung together from different contexts.

Conclusion

Because “Shadu-kam” is not a toponym at all but a misread adjective, there is no primary Persian work that can be cited for a “Land of Shadu-kam”. What you will find instead are innumerable instances of the epithet šâdkâm—“blissful, prosperous”—used of Paradise, the realm of the Peris, Spring gardens, happy kings, and so on. The western ‘legendary land’ was created by a chain of nineteenth-century misunderstandings and has no existence in the indigenous literature.