As a rule, in the real world, we use standardised names for people or places, rather than translating them into whatever our own language happens to be. Oftentimes, we probably don't know what a foreign-language name means in our own language, but even in cases where we do, we still use standardised names for people or places because it makes things more straightforward and helps keep miscommunications to a minimum.
Star Trek isn't the real world, but there's evidence to suggest that the same thing applies. For example, in a TNG episode, Picard stated in a captain's log entry that he'd learned the name Lal means "beloved" in Hindi. The fact that he apparently learned what the name meant after speaking it a number of times earlier in the episode suggests that it wasn't automatically translated by the Universal Translator (UT), otherwise "Beloved" is presumably what he'd have heard to begin with.
PICARD: Captain's log, supplemental. We are holding position pending the arrival of Admiral Haftel from Starfleet Research. Commander Data is completing his final neural transfers to the android he has named Lal, which I have learned, in the language Hindi means beloved.
In a DS9 episode, Odo and Laas explained to one another what their names means in the native languages of those names, which doesn't make sense as a conversation if you assume names are automatically translated by the UT.
ODO: You haven't told me your name.
LAAS: The Varalans called me Laas. In their language it means changeable. Not very imaginative, is it?
ODO: At least it's appropriate. My name means unknown sample. The scientist who found me didn't know what I was.
Star Trek: Deep Space Nine - S07E14 - "Chimera"
And in a Voyager episode, Ensign Samantha Wildman, Kes and the Doctor discussed various names and their meanings in other languages, which, again, doesn't make sense as a conversation if you assume names are automatically translated by the UT.
(Ensign Wildman is having a pre-natal check-up.)
WILDMAN: I've been considering naming him after my husband. It's been a tradition in his family for over five generations.
KES: I'm sure he'd be very pleased.
WILDMAN: My husband's name is Greskrendtregk. He's Ktarian.
EMH: Choosing a name is no easy matter. I speak from experience.
WILDMAN: Have you had any progress, Doctor?
EMH: I've reviewed historical, literary and anthropological databases from over five hundred worlds and have yet to find a suitable name. However, I may want to give some thought to Greskrendtregk.
WILDMAN: To be honest, I've been thinking of something simpler. What do you think of Cameron?
KES: I like it.
EMH: Cameron, from the ancient Celtic term for one whose nose is bent.
WILDMAN: What about Frederick?
EMH: **Frederick. Very distinguished. However, it bears a close resemblance to a rather impolite term on the Bolian homeworld.
WILDMAN: It doesn't have to be a human name. I like Sural. It's Vulcan.
EMH: Yes, unfortunately it was also the name of a dictator on Sakura Prime, famed for beheading his rivals, and his parents.
KES: You won't have any objection to Benaren.
EMH: You're right. I've never heard that name before.
WILDMAN: I think it's lovely. Is it Ocampan?
KES: Benaren was my father's name. He was the greatest inspiration of my life.
Star Trek: Voyager - S02E17 - "Dreadnought"
It's also worth noting that the UT apparently wasn't used on Archer's or Kirk's ships as standard, and that Starfleet officers apparently spoke in English by default, as established in this answer. As such, we can probably take it as read that when alien names such as "T'Pol" or "Spock" were spoken by human officers, they were likely being said as-is, rather than being translated.
