I don't know how much you've researched this, but:
On 19 April 2018, the King of Swaziland Mswati III announced that the
Kingdom of Swaziland had renamed itself the Kingdom of eSwatini to
mark the 50th anniversary of Swazi independence. The new name,
eSwatini, means "land of the Swazis" in Swazi, and was partially
intended to prevent confusion with the similarly named
Switzerland. However, the country's common name in English
We can see the same phenomenon recurring in other parts of the language:
Months in English and Swazi:
January -- uBhimbidvwane
February -- iNdlovana
April -- uMabasa
May -- iNkhwenkhweti
July -- uKholwane
August -- iNgci
October -- iMphala
November -- Lweti
Though as I've skimmed through more Swazi text, it seems most common with names, which I think is why they are common in the months of the year.
Note: Before my edit I had referred to Swazi spelling as a transliteration to English. This is definitely not correct, it's a "transcription" using the Latin script.
I'm unaware why these words were transcribed in this way using Latin characters to represent their language. I have absolutely no idea what a lowercase letter followed by an uppercase letter means in Swazi.
The alphabet can be seen here: Swazi alphabet
As to whether to capitalise these words at the beginning of a sentence, it's just a fact that this is dependent on style requirements/preferences and I'm afraid there don't seem to be universal English rules. Here is a section of the BBC's style guide in relation to this matter:
We treat most company names as though their punctuation were
conventional (eg: 'easyJet' is Easyjet). But there are specific
exceptions (eg: PricewaterhouseCoopers, iMac, NatWest), and one
general exception: that we do use a lower case 'e' at the start of a
name, where it stands for 'electronic' (eg eBay). If in doubt, check
with the Business team.
eBay - lower case 'e', and upper case 'B', except at the start of
sentences, where it should be written 'EBay'; but headlines can begin
iMac, iPhone, iPad, iPod, iTunes - lower case 'i', followed by
capital, except at the start of a sentence, where it should be IMac,
BBC Style Guide article
I also found what looks like a blog which discusses this with reference to the Chicago Manual of Style and The Associated Press Stylebook:
The Chicago Manual of Style has this to say: “Brand names or names of
companies that are spelled with a lowercase initial letter followed by
a capital letter (eBay, iPod, iPhone, etc.) need not be capitalized at
the beginning of a sentence or heading, though some editors may prefer
On the other hand, The Associated Press Stylebook states that writers
must capitalize the first letter – Ipad, Iphone, Ebay – because one
simply cannot start a sentence with lowercase letter.
Wikipedia’s Manual of Style suggests rephrasing to avoid beginning
sentences with initial lower case names.
Link to blog entry
Where I worked our rule was that sentences beginning with iPhone or eBay should remain as they are, that is, no capitalisation of the 'i' or 'e'.
As to the idea that to use our own English spelling of a foreign word is offensive, I find that rather ridiculous. Here's a list of discrepancies in the naming of places by natives and outsiders, and you can decide whether this is offensive, chauvinistic, or merely a result of historical events:
Japan/Nippon or Nihon
I have opinions about using "Eswatini" instead of "eSwatini", or circumventing the problem by avoiding the use of the word to begin a sentence, but this answer is long enough, and nobody cares anyway.