Learn English – How to tell the difference between proper nouns and regular nouns (in certain ambiguous cases)

Proper nouns should name specific people, places or things - "specific" being the key word here. In some cases specificity is immediately apparent, e.g. in the term "Singapore Airlines" (after all, there is only one airline with that name!).

In other cases, there is a grey area and I would say that fame/notoriety also plays a role in determining specificity. To use your example, one would refer to the Guantanamo letters if they don't contain any content that is particularly newsworthy. If, on the other hand, these letters happen to disclose some salient information that could result in a political scandal, then these letters would quickly garner attention and become intimately linked to this political scandal in the minds of people. Such a link would imbue the letters with a specific quality that would warrant the use of a proper noun, i.e. the Guantanamo Letters.

Thus, some common nouns can become proper nouns over time as they gain specificity in the minds of people. This can be a very organic process that can leave plenty of room for interpretation as to whether something should be considered a proper noun or not.

As you said, "culture [is] a generic noun with a proper modifier". In such cases, as long as the generic noun is not part of the proper name (i.e. part of the name Somali), you should not capitalize it.

I am proud to share Somali culture with the community.