In Nathan's parable (2 Samuel 12:1-6), only two persons were identified; that the rich man was king David, and the poor man was Uriah. The parable staged how a rich man who had power bullying the poor. As Nathan knew, David would surely condemn the rich man, then he could bring David to wake up from his righteousness.
The little ewe lamb was not Bethsheba. The parable staged both the poor and the rich loved their own flock. The poor afforded only one little ewe lamb who grew up with him and his children (vv12:3), but the rich had so many but reluctant to offer one as meal for the traveler (vv12:4). Instead he took the only one from the poor.
So the parable was to condemn David abused his power as king, that Nathan declared the Lord said:
7 Then Nathan said to David, “You are the man! This is what the Lord, the God of Israel, says: ‘I anointed you king over Israel, and I delivered you from the hand of Saul.
8 I gave your master’s house to you, and your master’s wives into your arms. I gave you all Israel and Judah. And if all this had been too little, I would have given you even more.
9 Why did you despise the word of the Lord by doing what is evil in his eyes? You struck down Uriah the Hittite with the sword and took his wife to be your own. You killed him with the sword of the Ammonites.
Who is the traveler in the parable?
The answer is 'nobody'. This role staged the necessity the rich had to offer the traveler a meal, that developed into the rich took the poor man's sheep.
The rich man had to treat the traveler well as all Israelites will know the Lord reminded them again and again that they should not mistreat a foreigner/traveler, for they were once foreigners in Egypt (Exo 22:21; 23:9; Lev 19:34; Deu 10:19). Abraham and Lot had received travelers without knowing they were angels (Gen 18:2-8; Gen 19:1-3). In the book of Hebrews, it wrote;
2 Do not forget to show hospitality to strangers, for by so doing some people have shown hospitality to angels without knowing it. (Hebrews 13:2 NIV)
Job also saw it as his righteousness
32 but no stranger had to spend the night in the street,
for my door was always open to the traveler— (Job 31:32 NIV)