There are three Raam in Hindu scriptures -
(1) Shree Raam - son of King Dasharath;
(2) Parashuraam - son of Maharshi Jamadagni and Renukaa
(3) Balaraam - the son of Vasudev and Rohinee.

At many places one can find only Raam, then how to differentiate them? That is why whoever takes delight in whatever that word has been added to Raam in front of it. Shree Raam takes delight in Shree or Lakshmee that is why He is called Shree Raam. Parashuraam takes delight in his Parashu (Pharasaa or axe) that is why Parashu has been added to his name. And Balaraam takes delight in his might, that is why Bal (might, or power) has been to his name.

Meaning of Raam Word
Raam word is composed of three letters - Ra + A + M. And these are the three seed-letters representing the Fire-god, the Sun-god and the Moon-god (Ra, A and Ma respectively). If put in other words, is that Ra, A and Ma can be said to be the origin of Vairaagya (dispassion) , Gyaan (wisdom) and Bhakti (devotion) respectively. This is why it has been said -

Rakaar hetur Vairaagyam Paramam Yachch kathyate
Akaaro Gyaan hetushch Makaaro Bhakti Hetkam  (Mahaa Raamaayan - 52:65)

Tulasee Daas Jee has also said these virtues of Fire, Sun and Moon in Raam-Naam in his Raam Charit Maanas as --

The virtue of Fire - जासु नाम पावक अघ तूला [Maanas 2.248]
The Lord whose Name Itself is a fire to the cotton of sins!

The virtue of Sun - जासु नाम भ्रम तिमिर पतंगा [Maanas 1.116]
The Lord whose very Name is like the sun to the darkness of illusion!

The virtue of Moon - राका रजनी भगति तव राम नाम सोइ सोम [Maanas 3.42]
May the name Raam shine as the Moon in the cloudless sky of your devotee’s heart during the Full Moon night of devotion to You!

Names of Shree Raam
Jaanakee-Vallabh - Husband or dear of Jaanakee
Kaushalyaa-nandan - Son of Kaushalyaa
Raaghav
Raghu-nandan - Descendent of Raghu
Raghukul-tilak - Respectable in Raghu Vansh
Raghunaayak - Leader of Raghu Vansh
Raghuraaj - King of Raghu Vansh
Raghuvar - Best among Raghu Vansh people
Raghuveer - Brave among Raghu Vansh people

Raamaaya Raambhadraaya Raamchandraaya Vedhasey
Raghunaathaaya Naathaaya Seetaayaah Pataye Namah

This Mantra is a part of Raam Rakshaa Stotra. Who does Jaap of this Mantra he attains Vishnu's Saayujya.
[Padm Puraan, p 998]