(disclaimer: not an expert on linguistics or etymology, just playing around with dictionaries)
Suppose humanity were to join the Galactic League of Sophonts. What would be the official name of our species? Hopefully the GLS will respect endonyms as much as possible, but the English word "humankind" won't do (I'm assuming English as de facto lingua franca of Earth; not a fan of that but it is what it is): alien species aren't going to have a local translation for "human", and most probably won't be able to pronounce Earth languages. So we need to find a way to translate "human" into roots as planet-neutral as possible.
Now, the English word human comes, via Latin humanus, from Proto-Indo-European *ǵʰm̥mṓ, which in turn was derived from *dʰéǵʰōm, meaning "earth" or "ground" (humanus could be interpreted as the adjectival form of humus, though in fact the two words derived independently from P-I-E). A suitable English-based but planet-neutral translation for "humans", therefore, could be Those of the Ground. This is also the case for all Latin-derived languages.
What of other major languages? I'd have expected for Hindi to have similar lines, and Hindi manuṣya मनुष्य looks a lot like humanus, but from what I find it seems unrelated, and comes from manu मनु meaning either "man" (with an unanalyzed P.I.E. etymology *mon, from which also "man") or "thinking, wise". Our Hindi-based name is The Wise Ones.
Russian čelovek челове́к comes from a Proto-Slavic word translated as "child of a clan", in turn from two P.I.E. roots *(s)kelh- and *kʷel-, translated respectively as "group of people" and "to travel/roll around". Our Russian-based name is The Wandering Tribe.
Arabic ‘insān إِنْسَان is a nominalized from verb ‘anisa أَنِسَ , which I see translated as either "to perceive/comprehend" or "to be comfortable/enjoy". I assume the first meaning is the relevant one: our Arabic-based name is The Understanding Ones. (Though The Comfortable Ones is also nice.)
Hebrew adam אָדָם also seems related to the ground, though indirectly: the Proto-Semitic root *dam means "blood", and hence refers to red things, such as clay or human bodies. Our Hebrew-based name is The Red Ones ("The Bloody Ones" wouldn't be very diplomatic, though our fellow sophonts might not have the same reactions as us. EDIT: But "The Bloodied Ones" would be different still, and probably fairer to the language.)
Chinese rén 人 is of unclear derivation; I see the main Proto-Sino-Tibetan candidates are *snaj "nearby" (in the sense of "relatives") and *s/k-niŋ "heart/mind/kindness", via Old Chinese nyin. I will pick the latter and assert that our Chinese-based name is The Kind Ones.
Japanese hito 人 runs into a wall: the Proto-Japonic etymology *pitə also just means "person". However, there is an alternate word ningen 人間 of Chinese derivation, which sends us back to the previous.
Swahili mtu is in a similar position: its Proto-Bantu source *mʊ̀ntʊ̀ means either "person" or "someone". However, Swahili also adopted binadamu "son of Adam" from Arabic, so I guess the choice is between the Arabic or Hebrew name. Similarly, Turkish got insan from Arabic.
Indonesian orang, intriguingly, is said to come from Proto-Malayo-Polynesian *uʀaŋ, meaning "outsider". Our Indonesian-based name, The Outsiders, comes ready-made. (Indonesian also got manusia from Hindi and insan from Arabic, so, if aliens decide to land on Java on account of being the most densely populated major island on Earth, we're set with names.)
brazenautomaton
