I think um means around, but German uses it for saying the time. Would the following expression be wrong?
A: Wie spät ist es?
B: Jetzt ist es schon um 20:00 Uhr.
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It is wrong.
If you want to say what time it is, simply say
Jetzt ist es schon 20:00 Uhr
The "um" would be wrong in this case. It is used, when you talk about the time of an event
Ich gehe heute um 11:30 in den Mittag
In Addition to that, if you want to tell the current time, but you don't know it exactly, then you would say
Jetzt ist es um die 20:00 Uhr
"um die" in this case has a similar meaning to "ungefähr".
Putting the context given away, the sentence can be correct for every native German speaker.
Example: Think of a recurring event that used to start at around 3 PM. Then the organizer decided that 3 PM is not a good time and moved it to, say, 5 PM. And now, eventually, they moved it again to an even later time — 8 PM that is.
Then the sentence "Jetzt ist es schon um 8 Uhr."1, most likely said in a frustrated voice, is perfectly valid. Note that jetzt doesn't refer to at this moment but to at the present time. And um clearly indicates that it is not necessarily an exact time.
Your given context, however, is a little weird. You refer to the time right now. You would give either the precise time (it's 3 minutes to 8), or an approximate time either without any indication that it isn't exact (it's 8) or with a hint that it's not too precise (it's shortly before 8).
While um certainly fits the third case (usually with a definite article), it's not common at all, except you don't know the exact time. It might be that some German (or Austrian or Swiss, for that matter) use it colloquially more frequently even if they know the exact time, but I don't know nothing about that.
So, if the context is that that current time is being asked, don't use um.
1 In the scenario I described above, erst would be more likely to be used over schon. Luckily, that doesn't weaken my argument at all. Actually, you would possibly even say "Jetzt ist es schon erst um 8 Uhr.", but that's not of matter in respect to the question.
As many answers have pointed out, um preceding a time usually means at exactly that given time. And using that intended meaning, your example would be wrong since the correct way to say it would be without um:
Jetzt ist es schon acht Uhr.
However some regional and dialectal language usage may also use um or related words to indicate somewhere around that exact time. Bavarian would most often use something sounding like umara — in fact, I once received an e-mail in Bavarian whose subject line was:
Gardn Party Samsdog umara viere. [sic]
Here, umara, a variant of um, is indeed used to say around, so the party would start at four-ish. Most Germans would probably use um … herum to express this, though, so using um to express around or -ish is often misunderstood.