There is a famous mantra of Lord Rama which explains how different living entities related to Him and how the Lord revealed Himself according to the relation. It was composed by Vaishta Muni and discussed between Mother Parvati and Lord Shiva in the Padma purana (Uma Maheswara Samvada 254-61). Mother Parvathi Devi keeps chanting this mantra always even in her sleep and this makes her very dear to Lord Shiva, who is the topmost Vaishnava.
raamaaya raama bhadraaya raamachandraaya vedase
raghunaathaaya naathaaya seethaaya pathaye namah
Raamaaya:- For Dasaratha, He is dear "Raama". Although He was named Ramachandra, Dasaratha had the privilege of calling him affectionately as "Raama". It shows the closeness in relationship between father and son.
Raamabhadraaya:- For spiritual seekers, Lord Rama is the bestowerof the desired benedictions according to their desire. And for his pure devotees, He gives the most auspicious benediction which is entry into spiritual world. So the scriptures advise all spiritual seekers to worship Lord Rama and since He blesses them with auspiciousness according to their approach for them, He is Ramabhadra ('Bhadra' means auspiciousness).
Raama Chandraaya:- For mother Kausalya, Kaikeyi and other women, He was Ramachandra because His beauty was pleasing like moon. The Ramayana states 'chandra kanthaananam raamam atiiva priya darshanam' - Lord Rama's face is like that of the moon and very pleasing to those who see Him.
Vedhase:- For great sages like Jamadagni, Vasishta, Viswamitra etc., the Lord revelaed Himself as the Supreme Absolute truth, Ultimate Reality (para tattva). More than being the son of Dasarata and Kousalya’ they realized Him as the creator of everything. Therefore they address Him as 'vedhase', - the omniscient creator.
Raghunaathaya:- According to the subjects of Ayodhya, Rama is an excellent king. So they saw Him as the best of Kings of Raghu vamsa (Raghunatha).
Naathaaya:- 'naatha' means husband or master. Mother Sita saw Him as her beloved husband and eternal consort. And devotees like Hanumanji, Sugreeva, Vibheeshana, Jambavan, Guha etc., saw Him as their eternal master and Lord.
Sitaayah pathaye:- For the subjects of Mithila He was consort of their princess Sita.
As we read this verse we can see that, although the Lord is versatile each one conceives one aspect according to their relation with Him. Thus the Lord possesses multi-faceted personality. The important thing is to re-estbalish our relation with Him and this is possible by pure devotional service, without hidden material agendas.