Kernix..out at sea and away from shipping lanes, most single handers sllep comfortably while the boat continues on under wind vane steering. Closer to shore or in the lanes, many use a radar range alarm to alert them when anything is nearby. Others power nap continuously using a kitchen timer to wake them every 15 minutes for a look around. Some will heave to and others will keep sailing. Everyone is different as is every boat so sailors work out what seems to be best for them...but we all need sleep.
We we are double handing on a passage in our boat, my wife and I will take turns napping during the day which we find very important to being alert at night....but not on any set schedule...then we take 3 hour watches generally at night but if I'm wide awake I'll extend mine so she doesn't have to get up and she does the same. In heavy weather we cut the watches down to 2 hours in darkness and I often will sleep in the cockpit to be close at hand. Again...no set rules...just what works for us.