Slackware - Slackware’s name is a reference to slack in the ideological sense, as espoused by the Church of the Subgenius (this one is a bit more complicated)
Debian - Deb(ra) and Ian, who founded the project
Ubuntu - is named after the Nguni philosophy of ubuntu, which Canonical indicates means “humanity to others” with a connotation of “I am what I am because of who we all are”. Ubuntu is an African word, has two parts, ubu and ntu, the zulu word for person is umu + ntu, the ubu prefix indicates it’s abstract which is how it comes to mean ‘humanity’.
Fedora - a volunteer project that provided extra software for the Red Hat Linux distribution, got the name from the characteristic fedora hat used in Red Hat’s “Shadowman” logo (as a nice side note Fedora can translate to “gift of God”)
RHEL - Red Hat Enterprise Linux, Red Hat got its name from founder Marc Ewing who wore a red Cornell University lacrosse hat, given to him by his grandfather and he used to name his software projects Red Hat, Red Hat 1, Red Hat 2…just to differentiate from his friends
CentOS - Community Enterprise Operating System
Gentoo - it’s a penguin, pTHE fastest penguin, (see Linux penguin logo), originally named Enoch Linux after a biblical figure who lived for 365 years
Manjaro - Kilimanjaro, the mountain that the founder of Manjaro climbed
SUSE - Software-und System-Entwicklung, german for Software and System Development
Mandrake - judging by the logo this can be related to Mandrake the magician
Mandriva - a combination of two companies names, MandrakeSoft and Conectiva
Kali - originally, it was designed with a focus on kernel auditing, from which it got its name Kernel Auditing LInux
Zorin - is the last name of the brothers who created it, also Zorin in Sanskrit is/was a name given to boys meaning strong or powerful
Deepin - name of a chinese company, probable meaning: inflaming, illuminating, exciting
Bodhi - the state of enlightenment attained by a Buddhist who has practiced the Eightfold Path and achieved salvation (I might have to try this one)
Devuan - (De)bian + VUAn (Veteran Unix Admins)
Knoppix - got the name from the developer Klaus Knopper, also Adriane KNOPPIX “subversion” which has a screen reader for blind people, named after his wife who is blind
MX Linux - The name comes from the combination of (M)epis Linux (the name of the company has no particular meaning) and anti(X) Linux both based on the older MEPIS distributions.
Arch - the creator liked the word’s meaning of “the principal, the best,” as in “arch-enemy”
siduction - a combination of sid (yeah thats Sid from Toy Story), codename for Debian unstable branch and the word seduction (after reading about it, siduction sounds like a better improved version of sid)
Pop!_OS - it’s a semi-joke, “Pop!” = “Pop, Bang!” just like “#!” = Crunch Bang, that’s why it’s always given with the weird punctuation in the name. You start off a shell script with a shebang and you start your OS with an exciting pop bang.
Void - name comes from it’s lack of packages and a project leader (pun intended) - Void comes from the C literal “void”, the name was chosen rather randomly and has no deeper meaning
Feren OS - “I just honestly took Heron and BS’d up a word that rhymes with it.” - said by the OS Developer
NixOS - niks is dutch for nothing, got converted to nix in english, prefix OS added later
GNU - stands for “GNU is Not Unix”
Alpine - originally stood for A Linux Powered Integrated Network Engine
Mint - the developer said: Mint is cold, it’s short, it’s fresh, it’s easy to type and to remember and in English it even means “cool”, “good condition”, “perfect” + also his favorite non-alcoholic drink, smell and flavour
Bedrock Linux - synonym for base, foundation on which parts of other distros are placed (other proposed names were Foundation, Frame and Scaffolding)
Mageia - (successor of Mandriva), the Greek term mageía (μαγεία) means enchantment, fascination, glamour, wizardry
Ututo - after an argentinian small lizard related to geckos, this was the first fully free GNU/Linux OS recognized by the GNU project
Android - named so because one of the founders, Andy Rubin, who liked robots and was nicknamed Android while working at Apple
Artix - from the official FAQ: It’s complicated. But “The Art of Linux” sounds nice.
DSL - Damn Small Linux named so because of its size, the iso being just under 51MB (just as a curiosity I’ll add Core weighing in at just 11MB and TinyCore at 16MB)
Garuda - indian name meaning “carrying great burdens”, “the sacred bird that carries Vishnu” and “heavenly eagle”(check logo)
PhysixProject - Physics, as in Science, breaks things down to their most basic processes (plus it sounded clever at the time) said the developer