Yes, japa of a mantra obtained from a Guru is extremely beneficial.
Repeat It and Contemplate Upon Its Meaning.
Patanjali's Yoga Sutra I.28
It stands for OM in the Yoga Sutra.
Sri Ramakrishna stood up. Referring to japa, he said to a devotee:
"Japa means silently repeating God's name in solitude. When you chant
His name with single-minded devotion you can see God's form and
realize Him. Suppose there is a piece of timber sunk in the water of
the Ganges and fastened with a chain to the bank. You proceed link by
link, holding to the chain, and you dive into the water and follow the
chain. Finally you are able to reach the timber. In the same way, by
repeating God's name you become absorbed in Him and finally realize
The Gospel of Sri Ramakrishna, The Master and Dr. Sarkar, October 24, 1885
Two issues of importance have been mentioned in the comment. The questioner feels that he has no Adhikara to chant a mantra because he is not a Brahmin. I am posting below Swami Vivekananda's opinion of such a doctrine. The questioner can safely ignore the doctrine of adhikarivada.
In one of his question classes the talk drifted on to the
Adhikârivâda, or the doctrine of special rights and privileges, and
Swamiji in pointing out vehemently the evils that have resulted from
it spoke to the following effect:
With all my respects for the Rishis of yore, I cannot but denounce
their method in instructing the people. They always enjoined upon them
to do certain things but took care never to explain to them the reason
for it. This method was pernicious to the very core; and instead of
enabling men to attain the end, it laid upon their shoulders a mass of
meaningless nonsense. Their excuse for keeping the end hidden from
view was that the people could not have understood their real meaning
even if they had presented it to them, not being worthy recipients.
The Adhikarivada is the outcome of pure selfishness. They knew that by
this enlightenment on their special subject they would lose their
superior position of instructors to the people. Hence their endeavour
to support this theory. If you consider a man too weak to receive
these lessons, you should try the more to teach and educate him; you
should give him the advantage of more teaching, instead of less, to
train up his intellect, so as to enable him to comprehend the more
subtle problems. These advocates of Adhikarivada ignored the
tremendous fact of the infinite possibilities of the human soul. Every
man is capable of receiving knowledge if it is imparted in his own
language. A teacher who cannot convince others should weep on account
of his own inability to teach the people in their own language,
instead of cursing them and dooming them to live in ignorance and
superstition, setting up the plea that the higher knowledge is not for
them. Speak out the truth boldly, without any fear that it will puzzle
the weak. Men are selfish; they do not want others to come up to the
same level of their knowledge, for fear of losing their own privilege
and prestige over others. Their contention is that the knowledge of
the highest spiritual truths will bring about confusion in the
understanding of the weak-minded men, and so the Shloka goes:
"न बुद्धिभेदं जनयेदज्ञानां कर्मसङ्गिनाम् ।
जोषयेत्सर्वकर्माणि विद्वान्युक्तः समाचरन् ॥" (३-२६)
— "One should not unsettle the understanding of the ignorant, attached
to action (by teaching them Jnâna): the wise man, himself steadily
acting, should engage the ignorant in all work" (Gita, III. 26).
I cannot believe in the self-contradictory statement that light brings
greater darkness. It is like losing life in the ocean of
Sachchidânanda, in the ocean of Absolute Existence and Immortality.
How absurd! Knowledge means freedom from the errors which ignorance
leads to. Knowledge paving the way to error! Enlightenment leading to
confusion! Is it possible? Men are not bold enough to speak out broad
truths, for fear of losing the respect of the people. They try to make
a compromise between the real, eternal truths and the nonsensical
prejudices of the people, and thus set up the doctrine that Lokâchâras
(customs of the people) and Deshâchâras (customs of the country) must
be adhered to. No compromise! No whitewashing! No covering of corpses
beneath flowers! Throw away such texts as, "तथापि लोकाचारः — Yet the
customs of the people have to be followed." Nonsense! The result of
this sort of compromise is that the grand truths are soon buried under
heaps of rubbish, and the latter are eagerly held as real truths. Even
the grand truths of the Gita, so boldly preached by Shri Krishna,
received the gloss of compromise in the hands of future generations of
disciples, and the result is that the grandest scripture of the world
is now made to yield many things which lead men astray.
This attempt at compromise proceeds from arrant downright cowardice.
Be bold! My children should be brave, above all. Not the least
compromise on any account. Preach the highest truths broadcast. Do not
fear losing your respect or causing unhappy friction. Rest assured
that if you serve truth in spite of temptations to forsake it, you
will attain a heavenly strength in the face of which men will quail to
speak before you things which you do not believe to be true. People
will be convinced of what you will say to them if you can strictly
serve truth for fourteen years continually, without swerving from it.
Thus you will confer the greatest blessing on the masses, unshackle
their bondages, and uplift the whole nation.
The Complete Works of Swami Vivekananda, Volume 5, Notes from Lectures & Discourses, The Evils of Adhikarivada
The questioner wanted to know if he can chant Rama's name. Of course he can chant Rama's name. It is necessary to point out that initiation is necessary for most seekers to get the effect.
It is laid down by the Lord that there can be no moksha, liberation,
without diksha, initiation; and initiation cannot be there without a
Kularnava Tantra, Readings by M. P. Pandit, Chapter X, Diksha (Initiation)
I am adding this to clarify my position on nama japa. Any one who is only chanting the Name is doing parts of Bhakti Yoga. He might not need to do anything if he has a done a lot of good karma in the previous life and in the present life and he surrenders completely to God.
Abandoning dependence on all Dharmas, come to Me as the only refuge.
Grieve not; I will deliver you from all sins.
Most people do not have a good enough karmic history to be able to surrender completely to God. Hence most people need the help of mantra japa to make spiritual progress.