- You might only be able to tell through context
- The name Harper is more likely than the name Harber
- Australian English is non-rhotic, which makes the /p/ less distinct
- If your native language isn't English, or even Australian/NZ English, you might be less attuned to these differences, and you mightn't know what common/usual names are
If you're interested in a slightly more technical explanation...
The reason that we're hearing it as /b/ rather than /p/ is likely because the two things that we usually look for are absent:
- It's surrounded by voiced segments (vowels)
- There's no aspiration
What you have below are a spectrogram (above) and waveform (middle) with annotations (below) for Harper.
The main issue with stops - of any kind - is that they're relatively boring sounds, there's not much happening in them.
You can see striations at the base of the spectrogram where he pronounces the vowels, but not during /h/ and /p/ - these indicate voicing.
Also, Australian English is non-rhotic - the /r/ in Harper isn't pronounced. Were this pronounced by an American English speaker, for instance, where the /r/ is pronounced, the /p/ is much more obvious and distinct.
Obviously, this kind of answer is more at home on Linguistics.se, but I thought I'd throw this in because I find it really interesting, and it might actually be of use to any language learners who happen to be trained in some articulatory/perceptory phonetics.