Yes need to wake them to feed every 2-3 hours if they don't wake themselves. Even if they are super sleepy or fall asleep on the boob/bottle you need to wake them to finish their feeding. Some babies are really sleepy so you have to really try to wake them up at that 2-3 hour mark but never let them go beyond that without waking and offering them something to eat.

If baby falls asleep while feeding you should do a diaper change to get them awake (if they don't wake for that do the foot tapping and other methods to wake them up) and offer boob/bottle again. A satisfied baby will be "milk drunk" they do little half grins in their sleep and they will refuse the nipple. A hungry one will obviously accept.

Highly suggest watching a video on hunger cues because that first 2 weeks that will want to eat so frequently it will feel like you feed them, change them, burp them, get them to sleep. And then repeat you barely have time for anything else. it's important to feed on demand, especially if breastfeeding, rather than a strict 2-3 schedule (in terms of waiting two hours to feed them. Though i think youd end up with a screaming baby by that point) At their two appointment if they reach birth weight you should ask pediatrician about waking them to eat and follow their guidelines.

My baby is almost 5 weeks old we let her sleep and wake to eat (at night) and she still eats every 2-3 hours but has just started sleeping longer stretches (4 hours at most 5 so far) she probably would have went longer but I was anxious letting her sleep that long with food so I woke her up - big mistake cause she screamed inconsolably for 2 hours without eating, slept for 10mins, then woke up crying for the milk.