Dr Sharib says:
"Ar-Rahim is a general name. According to some scholars Ar-Rahim is
the One Who confers the minutest blessings and bestows grace
"To emulate the name you should exercise self-control and engage
yourself in the remembrance of God, the Almighty. You should try to be
good, kind, considerate helpful, loving and kind to the people.'"
He goes on to say that appropriate recitation can make a person safe
and secure from troubles, and can make the heart the abode of love.

see 'The 99 Most Beautiful Names of Allah' by Dr Zahurul Hassan Sharib

Some other references:

According to Al-Ghazali:

'(Man's) share in the name al-Rahim lies in not turning away from any
needy persons without meeting their needs to the extent of his ability, nor
turning away from any poor in his neighbourhood........And if he be unable
to do all that he should assist them by prayer or by showing grief on
account of their need, in sympathy and love towards them, as though
sharing in their misfortune and their need.'

Al-Ghazali - The Ninety-nine Beautiful Names of God. Trans. Burrel/Daher: ITS: 1992.)

Neither is any creature great or small,
Beyond His pity; which embraceth all,
Because His eye beholdeth all which are;
Sees without search and counteth without care.

Sir Edwin Arnold: Pearls of Faith. Ashraf. Publications.

'Refers to God's Mercy under the aspect of reaching into the world and
leading beyond the world and back to God.'

'..ar-Rehman .....is a name of the essence Ar-Rahim is one of the Names
that describe the Divine Qualities.'

(Concise Encyclopedia of Islam)
Bismillah ir Rehman ir Rahim
The Compassionate,
The Merciful, The Clement, The Ever-Merciful
(Ar-Raheem, al-Rahim)
Qur'an 2:143
'He it is Who sends blessings on you,
as do His angels, that He may bring
you out from the depths of darkness
into light. And He is full of mercy to
the believers.'  

Qur'an 33:43
'Huwallazi yusallii 'alaykum wa malaaa
- 'ikatuhuu liyukhrijakum - minaz
-Zulu-maati 'ilan-Nuur: wa kaana
bil-Mu-miniina Rahiimaa.'