OFFICIAL NAMES AND THE CONSTITUTION
This site uses the official names of the languages of South Africa as set out in Article 6 of the Constitution of South Africa (1996):

(1) The official languages of the Republic are Sepedi, Sesotho, Setswana, siSwati, Tshivenda, Xitsonga, Afrikaans,  English, isiNdebele, isiXhosa and isiZulu.

The only language name not used consistently is that of Sepedi which actually refers to a dialect within Northern Sotho and not the whole language. Therefore the English 'Northern Sotho' or equivalent 'Sesotho sa Leboa' in this language is preferred.

The usage of prefixes in the constitution is consistent to what is required by the grammar of the different languages. This implies not capitalising the prefix in the Nguni language (isi- or si-) in siSwati, isiNdebele, isiXhosa and isiZulu when they are written in a sentence when used alone or at the beginning of a sentence the first letter is capitalised. Take note that the first letter of the actual root language name is a capital therefore we use 'isiZulu' and not 'isizulu'.

Furthermore it is widely recognised that Southern Sotho is known as Sesotho - leaving out the prefix and using Sotho would be confusing as this is also the term used for the Sotho language family (Sesotho, Setswana and Northern Sotho). It would therefore be senseless having the prefix for some languages but not for others.

The South African Concise Oxford Dictionary (2002) lists both the traditional English (for example Zulu) and the official language name as found in the Constitution of South Africa and used by the speakers (for example isiZulu).

HISTORICAL NAMING OF AFRICAN LANGUAGES
Historically the names of African languages have been transliterated and adapted to suit the way European missionaries or colonisers could pronounce or portray using their own orthographies or interpretations. Hence there are a lot of variant spellings between different languages but even within ones. Sesotho has been known as Sotho, Suthu, Sutu, Soetoe (Afrikaans).

Historically the official languages would be written as follows in English: Pedi (Northern Sotho), Sotho (Southern Sotho), Tswana, Swati, Venda, Tsonga, Afrikaans, English, Ndebele, Xhosa and Zulu. These language names are examples of exonyms as they refer to a name assigned by speakers who do not necessarily use the language as their mother tongue. The official names as listed in the Constitution of South Africa would be examples of endonyms - names given by the speakers themselves.

ARGUMENTS AGAINST USING OFFICIAL NAMES
Apart from the already mentioned concerns with the use of Sepedi for the language Northern Sotho. It is argued that one should not say isiZulu for example because one would not use Deutsch or Français for German and French respectively when using the language names in English. Therefore some

Language and Society in Africa (Herbert, 1992:5-6):

Within the African Language Association of South Africa (ALASA) there have been occasionally been heated discussions regarding the appropriate English and Afrikaans names for the various African languages, in particular, whether the obligatory noun class prefix of the languages should transfer into European languages, for example, do we call the language Zulu or isiZulu? Standard usages has followed the principles laid down by the International Institute of African Languages and Cultures in the 1920s, namely that all names are used in their uninflected form in both adjectival and nominal contexts, for example a Zulu (not an umZulu), several Zulu (not several amaZulu), Zulu/the Zulu language (not isiZulu/the isiZulu language). This principle has been followed fairly generally in Cenral and Southern Africa, less generally in East Africa...
The argument has been made recently, however, that it is only the speakers of a language who have the right to name that entity. To deny speakers the right to name themselves, their language or their customs is, it is claimed, racist. The use of one or the other form of the language name (with or without the class prefix) has increasingly come to be associated with a political stance within the Africanist linguist profession in South Africa. However sympathetic one may be to the ideology of the argument, it fails on several accounts. First and foremost, it confuses meaning with structural facts of cross-linguistic transfer. English speakers reference to le français as French, to Cymraeg as Welsh or the Zulu speaker's reference (when speaking Zulu) to isiNgisi rather than English and to isiVenda rather than (tshi)Venda.

The Bantu languages of South Africa (In: Language and Social History) (Baily, 1995:34)

There is currently considerable inconsistency in the designation in English of Bantu language names, This is regrettable, for linguists should set an example of consistent usage for scholars in other fields, and the public at large to follow.
The language names used are generally of two or more syllables, and so the names are seldom uncomfortably short. Tshwa is an exception. It may be argued that the roots, such as 'Zulu, Swahili, Swati, Sotho', do not occur as free forms in the languages concerned. This is hardly relevant, as the issue is what is appropriate in English. The original consonants, vowel qualities, stress and tone of these words will in any case be distorted in English. If the prefix is taken over into English as a detail of grammar, then speakers of English will have to learn where to perform the morphological segmentation when they wish to form the ordinary ethnonym and adjective.

The Bantu languages: sociohistorical perspectives (In: Language in South Africa) (Herbert & Baily, 2002:74)

There is some ongoing debate within South Africa as to whether African language names should be cited with or without the language appropriate prefix, e.g. Zulu or isiZulu, Tsonga or Xitsonga/xiTsonga. Within this chapter, language names are cited in their most common forms within the scholarly literature, which are usually prefixless.