Thus spake the Sages:
Our ancient Sages and Rishis have glorified the Rama Nama.
Rama Nama gets exactly the same importance in Saguna Upasana (worshipping the Absolute Truth as a Being with a form) as does the Pranava ('Om') Mantra in Nirguna Upasana (worshipping the Absolute Truth as formless).
Rishi Manu shows that the Rama Nama has links to all the other mantras that ever exist.
In Syavana Smriti (Syavana is the name of a rishi), Syavana says that the Rama Nama is the essence of all the Vedas, Shastras, Itihasas and Puranas.
Sage Vasishta meditated on the Rama Nama for quite a long time. Hence he wanted to name the Almighty with the same Mantra that he had chanted.