Tracing a Surname

There's a pair of 4rd great grandparents that have been the topic of a few of these posts and the point of some of my frustrations with searching for their information.

They are Juan Carlos Gustavo and Julia/Balbina Lotten (and all their many alternations/alter-egos included) who according to documents immigrated from either Guadeloupe or Martinique (some documents mention Saint Thomas! -___-)

I decided to look at their grandchildren's birth records to trace their surnames and see how they've changed over time and how often they changed. The first apparently starts out at Gustave in 1885 but changes quickly to Gustavo and stays that way for the remainder of the documents. Sometimes Charles appears as their last name; both Gustave and Charles might not have even been their original surname! Here are the images of the surname "Gustave" across the years:

Gustave- 1885

Already "Gustavo" in 1887!

Still "Gustavo" at 1890- stays that way 

The second name starts out as Lotten and sometimes even looks like Lobben to me. I say though that the original was somewhere near Lotten instead of Lobben because every other alternative to the name includes a "T" rather than a "B" in its spelling. The name has had some crazy variations from Lotiz, to Sotin and everything in between. Here is the name also traced across some years:

"Lotten" or "Lobben"?- 1885

"Lote"- 1890

"Lotett"- 1893

"Loter"- 1895

"Lotis"- 1898

In the same year (1898) appear as "Lotiz"

"Soti"- 1899

The second surname has had many a variations throughout the years as we can see even within the span of two years the name can be changed very quickly. It all depended on 1) Who was speaking, 2) Who was recording and 3) Who cared to actually make it sound as close to the original name as possible. Even in 1920, in Alberto Gustavo y Lotten's census record his name appears as "Sotin", picture below.

1920 Census- Alberto Gustavo Sotin

Oddly enough, he also appears as Alberto Gustavo Perez in his 1910 Census and 1917 WWI Record.

Appears as "Gustavo Perez" instead of "Gustavo Lotten"

So I am all kinds of confused with what was the original spelling if they even got it right at all. The name to me sounds sort of French/German if I'm anywhere near right. 

Hopefully, I'll find their mother's death certificate (which I haven't been able to find yet) or maybe in some of the immigration records from the LDS, I'll be able to find it.