ShriRama was a purushottama. However he is linked only to Raghu, one of his ancestors but not Dilipa, Sagara, Ikshvaku, Bhagiratha, Aja, Dasharatha. Why Raghu is so important? Also after Rama, his sons are not referred as Raghus why?
This question is related to Describe the story of lunar race and solar race
In most of the cases, the name of a lineage changes after a Chakravarti Samrat. However this is not a hard and fast rule, they can continue with old name as well.
Lord Shri Rama's lineage can be called as Suryavanshi, Ikshvaku vanshi, Raghu vanshi or Raghav etc. And Lord Shri Rama can be called as
One who was born in the clan of Surya (Sun God), Suryavanshi Kshatriya
One who was born in the clan of Ikshvaku, Ikshvaku vanshi
One who was born in the clan of Mandhata, Mandhata vanshi
One who was born in the clan of Raghu, Raghu vanshi or Raghav
Hence, Lord Shri Rama is mentioned in Valmiki Ramayana as Ikshvaku vanshi, Mandhata vanshi, Raghu vanshi or Raghava and Dasharatha's son.
Why most of the time Raghava (Raghuvanshi) or Dasharatha's son?
Because Raghu was more recent Chakravarti king as compared to others in the lineage. And Dasharatha was his father.
Note: However, Valmiki Ramayana mention many kings in between Raghu and Dasharatha including Nahush and Yayati (who are Chandravanshi kings altogether as per other scriptures). Most of other sources tell only Aja in between Raghu and Dasharatha.
After Rama, this lineage had a name which was honored by the title Lord. So they followed Lord Shri Rama's name afterwards.
Due to Raghu's name the lineage came to be known as Raghu vansh or Raghava. Not only Rama but whoever was born in the lineage after Raghu can be referred as Raghu vanshi or Raghava i.e. Aja, Dashratha, Laxmana and Bharat too can be referred as Raghava.
Same is the case with Arjuna. He can be called Chandra vanshi, Puru vanshi, Bharat vanshi or Bharata, Kuru vanshi or Kaurava, son of Pandu or Pandava, son of Pratha (birth name of Kunti) or Parth, son of Kunti or Kauntey.
But most of the time he is called as Parth or Pandav as compared to other names as these names are derrived from his immediate previous generations.