Why Do We Recite Astothram or Saharanamam

According to the greatest Siddha our objective should be to realize our Godhood. For that we have to understand that in front of God, we are less than nothing. For that rather than keep saying that we are nothing, we should praise the lord. Slowly by this praise we realize that only God is supreme. That only God is the truth and that we are nothing but his creation that he makes to play games. That is the reason of praising God in Hinduism.
Praising God in many names or describing various attributes/functions of God by reciting Astotham or Shahasranamam not necessarily a sign of ignorance; it indicates an intimate knowledge of God.

For example, Eskimos have forty-eight different names for snow in their language because they know snow intimately in its different variations, not because they are ignorant of the fact that all snow is only one.

Effect of Praising God
Praising God makes every circumstance of our lives complete, essential, and eminently worthwhile.
God deserves to be praised and He is worthy to receive our praise.
By praising God, we are reminded of the Greatness of God!! His Power and presence in our lives is reinforced in our understanding.
Praise discharges strength in faith which causes God to move on our behalf.
Praising God also transforms the spiritual environment around us.
God inhibits in the atmosphere of praise.
Christians too believe in praising God:
‘Let everything that has breathe Praise the Lord” psalm150:6

We can give glory and praise to our God with the use of our physical bodies, with our hearts and mind, and with our deeds. There are many ways to praise our God and one of them is reciting Astothram or Saharanamam.
No matter how we praise our God and Worship Him, it should result in awe of God

Prayers are answered in most cases by the released will-power of the worshippers–power they have no idea is really theirs. Some prayers are answered by God or those he has designated to foster humanity in this way.

Reciting Astothram or Saharanamam is a form of Hindu Prayer

From ancient times, many Hindus in learned families daily recited the Sahasranama, or a similar set of prayer Shlokas of their chosen deity. (Such a collection of Shlokas which are used for recital purposes is generally called a Stotra.
In Sanskrit, sahasra means "a thousand" and nāma (nominative, the stem is nāman-) means "name". The compound is of the Bahuvrihi type and may be translated as "having a thousand names". In modern Hindi pronunciation, nāma is pronounced [na:m]. It is also pronounced sahasranāmam
Bhisma says that mankind will be free from all sorrows by chanting the Vishnu sahasranāma' which are the thousand names of the all-pervading Supreme Being Vishnu, who is the master of all the worlds, the supreme light, the essence of the universe and who is Brahman. All matter animate and inanimate resides in him and he in turn resides within all matter
Believers in the recitation of the Sahasranama claim that it brings unwavering calm of mind, complete freedom from stress and brings eternal knowledge.
One who reads this hymn every day with devotion and attention attains to peace of mind, patience, prosperity, mental stability, memory and reputation
Chanting mantras or reciting astothrams is one of the ways to stop the thought flow. We also imprint our needs in the subconscious mind when we recite. When we recite, the energy becomes concentrated and is focused in a particular mantra/ astothra. This focused energy is what becomes the bright deity and brings faith our needs.