Ganesha is known not by one name or two, but by many names, Each name has an explanation. Because of his elephant face he is called Gajanana ('Gaja' meaning elephant); as the leader of Shiva's Gana he is known as Gananayaka; he bestows boons on his devotees and so is Varasiddhi Vinayaka, he is Vidya Ganapati because he grants knowledge and wisdom; he is called Gowriputra because he was born by the grace of Parvati, Ekadanta because he has only one tusk, and Vighneshwara because he is the Lord of all obstacles - so he has many names.

Akhuratha - One With Mouse As His Charioteer
Alampata - The Eternal
Amit - One Who Has No Comparison
Anantachidrupamayam - Infinite And Consciousness Personified
Avaneesh - Master Of The Whole Earth
Avighna- Without Obstacles
Balaganapati - The Beloved Child
Bhalchandra - Sporting The Moon Crest
Bheema - Gigantic
Bhoopati - Lord Of The Lords
Bhoovanpati - Lord Of The Lords
Buddhinath - Lord Of Wisdom
Buddhipriya - Bestower Of Knowledge
Buddhividhata - God Of Wisdom
Chaturbhujeti - Four-Armed
Devadeva - Lord of All Lords
Devantakanashakarin - Destroyer Of Demons
Devavrata - Accepter of All Penances
Devendrashika - Protector Of the Gods
Dharmik - One Who Favours Charity
Dhoomravarna - Smoke-Coloured Body
Durja - The Invincible
Dvaimatura - Son Of Two Mothers
Ekaakshara - Of The Single Syllable
Ekadanta - He Of Single Tusk
Ekadrishta - Single-Tusked
Eshanputra - Son Of Shiva
Gadadhara - Wielder Of The Mace
Gajakarna - Elephant-Eyed
Gajanana - Elephant-Faced
Gajananeti - Elephant-Faced
Gajavakra - Elephant Trunk
Gajavaktra - Elephant-Mouthed
Ganadhakshya - Lord Of The Celestial Hordes
Ganadhyakshina - Lord Of The Celestials
Ganapati - Lord Of The Ganas
Gaurisuta - Son Of Gauri
Gunina - Lord Of All Virtues
Haridra - The Golden One
Heramba - Beloved Of The Mother
Kapil - Tawny-Coloured
Kaveesha - Lord Of Poets
Kirti - Lover Of Music
Kripakaram - Who Is Merciful
Krishapingaksha - Black- Yellowish -Brown -Eyed
Kshamakaram - Abode Of Forgiveness
Kshipra - Quick-Acting
Lambakarna - Large-Eared
Lambodara - Huge-Bellied
Mahabala - Extremely Strong
Mahaganapati - The Omnipotent And All-Powerful
Maheshwaram - Lord Of The Universe
Mangalamoorti - The Auspicious
Manomay - Conqueror Of One's Heart
Mritunjaya - Deathless
Mudakaram - Abode Of Joy
Muktidaya - Giver Of Eternal Peace
Musikvahan - He With The Mouse As His Vehicle
Nadapratithista - Lover Of Music
Namasthetu - Destroyer Of All Sins
Nandana - Son Of Lord Shiva
Nideeswaram - Master Of All Kinds Of Treasures
Pashin - One Who Sits Like A Rock
Pitambar - Wearer Of Yellow Clothes
Pramod - Lord Of The Place
Prathameshvar - One Who Holds The First Place
Purush - The Supreme Authority
Rakta - Red-coloured
Rudrapriya - Beloved Of Shiva
Sarvadevatman - Accepter Of Celestial Offerings
Sarvasiddhanta - Provider of Adeptness To His Disciples
Sarvatman - Blesser Of The Universe
Shambhavi - Son Of Parvati
Shashivarnam - Moon -Complexioned
Shoorpakarnai - Large-Eared
Shuban - One Who Is Auspicious
Shubhagunakanan - Mine Of All Virtues
Shweta - White Colour
Siddhidhata - Bestower Of Success
Siddhipriya - Bestower Of Boons
Siddhivinayaka - Bestower Of Success
Skandapoorvaja - Older Than Skanda
Sumukha - Of Auspicious And Pleasant Visage
Sureshwaram - Lord Of All The Gods
Swaroop - Lover Of Beauty
Tarun - The Youthful
Uddanda - Punisher Of Evil
Umaputra - Son Of Uma
Vakratunda - Askew-Trunked
Varaganapati - Bestower Of Boons
Varaprada - Granter Of Boons
Varadavinayaka - Bestower Of Bounty And Success
Veeraganapati - The Valiant Warrior
Vidyavaridhi - Repository Of All Knowledge
Vignahara - Destroyer Of Evil
Vignaharta -Destroyer Of Obstacles
Vighnanashin - Destroyer Of Obstacles
Vighnaraja - Lord Of All Obstacles
Vighnarajendra - Lord Of All Obstacles
Vighnavinashanaya - Destroyer Of All Afflictions
Vigneshwar - Lord Of All Obstacles
Vikat - Of The Monstrous Figure
Vinayaka - Lord Of All
Vishwamukha - Lord Of The Universe
Yagnakaya - Accepter of Sacrificial Fires
Yashaskaram - Giver Of Fame And Glory
Yashvasin - The Popular
Yogadhipa - Lover Of Meditation