Raghukul Reet sada chali aayi, Pran jaaye par Vachan Na jaayi"Shri Ram was known as Raghuvanshi because he belongs to Raghuvansh or Raghukul, a dynasty which was named after king Raghu.
This episode of Holy Tales by Himanshu Sharma will tell you how King Raghu kept his words for a brahmin who came to his doors for help.