Because Vader was a well-known individual in the Empire.
Vader quickly became a highly visible symbol of the Empire, serving as Palpatine’s fearsome enforcer.
He hunted down fugitive Jedi who had escaped Order 66, as well as ferreting out enemies both within and without.
Darth Vader - Databank (emphasis mine)
And if you are wondering how Kenobi knew Darth Vader was Anakin Skywalker, he saw it in the temple hologram.
OBI-WAN moves to a panel and flips some switches.
He sees a HOLOGRAM of ANAKIN slaughtering JEDI, including the YOUNG ONES.
OBI-WAN and YODA react.
OBI-WAN: (continuing)
It can't be . . .
It can't be . . .
As ANAKIN surveys the carnage, a DARK-ROBED SITH LORD enters.
ANAKIN turns to DARTH SIDIOUS and kneels before him.
ANAKIN:
The traitors have been taken care of, Lord Sidious.
DARTH SlDIOUS:
Good . . .
good . . . You have done well,
my new apprentice.
Do you feel your power growing?
ANAKIN:
Yes, My Master.
DARTH
SlDIOUS:
Now, Lord Vader, now go and bring peace to the Empire.
OBI-WAN watches in horror.
Tears well up in his eyes.
OBI-WAN:
I can't watch any more.
OBI-WAN switches off the hologram.
The TWO JEDI stand in silence for a few moments.
YODA:
Destroy the Sith, we must.
OBI-WAN:
Send me to kill the Emperor.
I will not kill Anakin.
YODA:
To fight this Lord Sidious, strong enough, you are not.
OBI-WAN:
He is like my brother ...
I cannot do it.
YODA:
Twisted by the dark side, young Skywalker has become.
The boy you trained, gone he is . . .
Consumed by Darth Vader.
Episode III: Revenge of the Sith
scifi.stackexchange.com/users/62201/amflare
First, Obi Wan knew Vader was Anakin.
As this question points out, he saw Palapatine address Anakin as "Vader" in a security hologram at the Jedi temple during the events of Revenge of the Sith.
Second, from this question , it was apparently common rumor that Vader was part machine:
It was that genuflecting obedience, the steadfast devotion to execute whatever task the Emperor assigned, that had given rise to so many rumors about Vader: that he was a counterpart to the Confederacy’s General Grievous the Emperor had been holding in reserve; that he was an augmented human or near-human Star Wars: Tarkin.
So even without considering Obi Wan's well developed force powers, it could be a reasonable statement to make.
scifi.stackexchange.com/users/89007/Harabeck
Vader is a famous figure in the Empire .
Although Obi-Wan is described as living as a hermit, he would have needed to keep some tabs on local Empire propaganda to help him stay hidden.
It is likely that almost everyone in Imperial territory knew what Darth Vader looks like (with his armor on, at least).
Obi-Wan would know that much too.
Obi-Wan is probably just guessing about Vader's cybernetic enhancements, but he has good reason to make the assumptions he does, because unlike most people, Obi-Wan knows the extent of Anakin's injuries .
Vader lost most of his limbs on Mustafar, yet he is seen walking and using hands.
Anyone who hears Vader speak knows he has a breathing apparatus, but most people probably think this is just part of the armor's function as a space suit.
Obi-Wan, though, knows where and how Anakin's lungs could have been damaged.
Given the medical technology of the series, it would have been safe for Obi-Wan to assume that Vader's limbs and lungs are cybernetic , because he just plain wouldn't have them otherwise.
scifi.stackexchange.com/users/17414/The Spooniest
As others have stated, surely there was Imperial propaganda that depicted Vaders image.
However it doesn't matter what Vader looked like in order for Obi-Wan to know him.
Obi-Wan and Vader sensed each other's presence on the Death Star before they met face to face.
Obi-Wan could have been wearing a snowman suit and Vader dressed as a toaster and they both would have known each other.
This was, after all, master and apprentice who spent years training and fighting together in the clone wars.
Obi-Wan also knows that Vader at that point has lost an arm and two legs from his battles, so in order for him to be still around he would have to be "more machine than man" now.
When Obi-Wan sees Vader he is standing in the corridor with his lightsaber ignited, and then walks up to Obi-Wan and starts talking.
How many Dark lords of the Sith would be walking around on the Death Star waiting for him?
Obi-Wan Kenobi vs Darth Vader
scifi.stackexchange.com/users/45543/Mykewlname
Vader hadn't seen Obi-Wan in years either.
The last time he had seen his former master he looked like Ewan McGregor.
Going by sight alone he would have been forgiven for failing to recognise him as the ageing Alec Guinness.
But of course Vader sensed his old master was in the vicinity long before he encountered him face to helmet.
If Vader could sense Obi-Wan's presence by the force alone, logically Obi-Wan could sense Vader/Anakin too.
Obi-Wan himself explained that the force " surrounds " and " penetrates " all living things.
If that is the case it is also logical that those who are sensitive to the force can sense both the outer appearance of another living thing as well as their inner person.
Obi-Wan could have therefore sensed that Anakin was "more machine than man" based on how the force surrounded and penetrated his remaining living tissue.
scifi.stackexchange.com/users/105362/Astralbee
How did Obi-Wan know what Vader looked like before he confronted him? "He is more machine now than man"
How did Obi-Wan know what Darth Vader looked like in Episode IV?
scifi.stackexchange.com
<star-wars><darth-vader><obi-wan-kenobi>
scifi.stackexchange.com/questions/195395
scifi.stackexchange.com/users/105304/Chris Lehnigk
Obi-Wan knew what Darth Vader looked like because Darth Vader was a well-known individual in the empire. It's quite possible that everyone knew what Darth Vader looked like. Aside from this, using the force, Vader and Obi-Wan were able to detect each other's presence aboard the Death Star long before they encountered each other. Darth Vader's apperance was familiar across the Empire through propaganda, but also Obi-Wan knew he was Anakin and therefore that he must be part machine due to Anakin's injuries. Obi-Wan would also have recognised Vader because of the link from their former relanship as master and apprentice.
Darth Vader was well known throughout the Empire and therefore anyone would have known what he looked like. First, Kenobe knew Vader was Anakin and secondly it was widely rumoured that Vader was part machiner. Kenobi would have known Vader's appearance from local Empire propaganda and he would have known Vader was part machine because he knew the extent of Anakin's injuries, which would have necessitated mechanical replacements. Despite the propaganda providing examples of Vader's appearance Kenobi would have sensed it was him because of their old relationship as master and apprentice.