Yes, she can disguise herself as another person.
When Harry first met Tonks, she told him that she was able to excel at Concealment and Disguise without having to study because she’s a Metamorphmagus.
“How did you do that?’ said Harry, gaping at her as she opened her eyes again.
‘I’m a Metamorphmagus,’ she said, looking back at her reflection and turning her head so that she could see her hair from all directions. ‘It means I can change my appearance at will,’ she added, spotting Harry’s puzzled expression in the mirror behind her. ‘I was born one. I got top marks in Concealment and Disguise during Auror training without any study at all, it was great.”
- Harry Potter and the Order of the Phoenix, Chapter 3 (The Advance Guard)
She does seem to be able to create unique identities for herself.
She disguised herself as an old woman to take Harry to Hogwarts, and go to Kings Cross with him.
“Where’s Tonks?’ Harry said, looking round as they went down the stone steps of number twelve, which vanished the moment they reached the pavement.
‘She’s waiting for us just up here,’ said Mrs Weasley stiffly, averting her eyes from the lolloping black dog beside Harry.
An old woman greeted them on the corner. She had tightly curled grey hair and wore a purple hat shaped like a pork pie.
‘Wotcher, Harry,’ she said, winking. ‘Better hurry up, hadn’t we, Molly?’ she added, checking her watch.”
- Harry Potter and the Order of the Phoenix, Chapter 10 (Luna Lovegood)
She also disguised herself as a different woman to leave Grimmauld Place and take Harry back to Hogwarts on the Knight Bus.
“Next moment, Harry found himself being shunted out into the icy winter air, with Tonks (today heavily disguised as a tall, tweedy woman with iron-grey hair) chivvying him down the steps.”
- Harry Potter and the Order of the Phoenix, Chapter 24 (Occlumency)
While it is possible that Tonks based these disguises off of women she’d seen, she didn’t need to be any specific person in either of those cases.
She probably can disguise herself as a man, though she didn’t.
Since she can transform herself into any kind of (human-ish) thing, it’s very likely that she can make herself appear male as well. Polyjuice Potion, another more limited form of appearance-changing magic, allows for different-gender transformation, since both Hermione and Fleur used it to turn into Harry. However, Tonks does seem to be able to transform her features individually, so even if she disguised herself as a man, she may possibly choose not to transform everything.
Despite this, there are no examples of her using a male disguise that we see. That may simply be because she’s more comfortable remaining female.
She can also do borderline nonhuman features.
Tonks used her Metamorphmagus skills as dinnertime entertainment, giving herself various odd noses, including a pig snout.
“Opposite Harry, Tonks was entertaining Hermione and Ginny by transforming her nose between mouthfuls. Screwing up her eyes each time with the same pained expression she had worn back in Harry’s bedroom, her nose swelled to a beak-like protuberance that resembled Snape’s, shrank to the size of a button mushroom and then sprouted a great deal of hair from each nostril. Apparently this was a regular mealtime entertainment, because Hermione and Ginny were soon requesting their favourite noses.
‘Do that one like a pig snout, Tonks.’
Tonks obliged, and Harry, looking up, had the fleeting impression that a female Dudley was grinning at him from across the table.”
- Harry Potter and the Order of the Phoenix, Chapter 5 (The
Order of the Phoenix)
It’s unclear how long she can keep the same appearance.
We don’t know how long Tonks can keep her transformed appearance without “redoing” it. She does usually keep her hair short and pink, which she uses her Metamorphmagus ability to do, but we don’t know if she eventually has to do anything to keep it that way.
Even so, she can most likely use it to go into hiding.
Tonks can transform rather quickly, so even if she has to do something to keep her transformed appearance the same, she could probably maintain it, similarly to how she typically keeps her hair transformed a specific way.
The only thing that seems likely to be the biggest problem with her using the ability to go into hiding is if during that time she experiences some kind of emotional turmoil, since that can stop her power from working like it did when she was upset over Lupin.