Look at this full text from Luke 4:40-42 (NIV): (references to Jesus in bold):
40 At sunset, the people brought to Jesus all who had various kinds of sickness, and laying his hands on each one, he healed them. 41 Moreover, demons came out of many people, shouting, “You are the Son of God!” But he rebuked them and would not allow them to speak, because they knew he was the Messiah.
42 At daybreak, Jesus went out to a solitary place. The people were looking for him and when they came to where he was, they tried to keep him from leaving them.
This illustration shows the problems with the simple idea that a pronoun is used in English when the participant has been named in the previous sentence. There are two problems with this idea as applied to this passage.
First, there is a sentence without Jesus at the start of verse 41 referring to the demons, and we still have a pronoun for Jesus in the second half of the verse. This is fairly straightforward, as the reference to Jesus is still quite close, and the participants that interrupt, the demons, are plural and thus cannot be the referent for "he" in the next sentence.
Second, and perhaps more interestingly, in verse 42, we have a full name for Jesus, even though he was mentioned in the previous sentence,. He is even the subject in both cases, something that is sometimes important for pronoun reference in English. So, even though a pronoun would be normal (and even expected in this context), we have a full name. Why is this? In this case, the use of a full name instead of a pronoun is one way of showing the break to a new episode, a new "paragraph". This is also indicated by the fronted expression "At daybreak," which makes the new time explicit.