Also known as Siri Gaitri Mantra
The akshara 'Ra' represents light or fire. This is not just the light of energy but also of knowledge, of enlightenment.
The akshara 'Ma' represents the 'Mind' (manas). Also extends to the self, (atma) and down to 'Man.'
'RA MA' therefore is the 'man in search of/ going towards the light, or, enlightenment; the atma towards the paramatma.
Thus Rama can also mean 'to be in bliss', in enlightenment etc.
In the Puranic epic Ramayana, Rama was the scion of the Solar Dynasty (Suryavamshi) - so perhaps Rama - the 'Man of the Sun'
In the story 'Ramayana', Rama is the model of the 'Perfect man' (Purushothama) and his [perfect] way of life until he merges with the Supreme. Thus 'Rama Yana' ('yana' meaning 'the way') is the 'Way of Rama'