Well, about as sick and tired as I am of everyone and their mother thinking that Senji's first name is... ah, Senji, it's quite understandable that they would assume that. After all, everyone calls him Senji, it sounds like a first name after all, and Kiyomasa does indeed sound like a last name. However- after extensive research, why yes I did have to do research on this since no one seems to understand, I found a lot of points about it.
1. Officially translated by FUNIMATION
He says his name here, and when he voices it he speaks and says his name in the standard, last name first name order, but of course the subs come up as 'Kiyomasa Senji'
In case that's not enough-
Ganta's name is translated in this order as well, but of course.
2. That being said, the kanji for Senji's name is also 千地 清正 ...but, to people that can't read that-
The first set of kanji is 'Senji' while the second is 'Kiyomasa'... once again, an example using Ganta's kanji is 五十嵐 丸太 with Igarashi Ganta being the order that the kanji goes. Yet again, this shows that his first name is Kiyomasa, everyone in the canon simply refers to him as Senji.
3. A part where all the names are displayed in certain orders as well:
...whoever spelled all the names was apparently drunk however....
4. In any case, the way Senji is named is very old fashioned, and I looked up the name 'Kiyomasa' and found that -masa is generally added on to first name, rarely on to last. The way he's named is like that of a samurai, what with the first name being longer than the last, much like Sanosuke Harada.
Looking up name meanings helps as well, since this is all on a first name meanings site:
Masculine and endowed with a certain magnetism, Kiyomasa emanates an air of strength. He is courageous and assertive, although he is also quite wary. This is undoubtedly related to his shyness and emotional fragility - a real Achilles´ heel which affects his mood and level of enthusiasm. This can occasionally result in outbursts of anger if he doesn't feel that he has been fully understood.
5. To help reinforce this, there's also another character in the canon that is always referred to by his last name. Tamaki's first name is Tsunenaga, however no one refers to him as such- it's even evident by this character page:
On this the kanji states 'Tamaki Tsunenaga' in the last name first name order as well.
And to go along with that, here's Senji's:
Showing the fact that they're both referred to by their last names.
So yes, officially his name was translated as Kiyomasa Senji by funimation, and several other factors here that lead me to believe his name is indeed Kiyomasa, however the entire fandom and even characters in canon all refer to him as Senji. This leads to a lot of confusion, but I believe that Kiyomasa and Senji are both first names, much like a Robert Andrew scenario. I'll take this all back if I'm proven wrong, but I'm about 98% sure his first name is Kiyomasa after all this, my only doubts come from the fandom constantly referring to him as Senji and ignoring these facts.