The Following are some of the Common Names of Lord Ganesh

Dhoomraketu,  Sumukha,  Ekadantha,  Gajakarnaka,  Lambodara,  Vignaraja,  Ganadhyaksha,  Phalachandra,  Gajanana,  Vinayaka, Vakratunda,   Siddhivinayaka,  Surpakarna,  Heramba,  Skandapurvaja,  Kapila and Vigneshwara.   He is also known by many as Maha-Ganapathi.

His Mantra is Aum Gung Ganapathaye Namah.

Spiritual aspirants who worship Ganesh as their Deity repeat this Mantra or AUM Sri Ganeshaya Namah.

The devotees of Ganesh also do Japa of the Ganesh Gayatri Mantra. This is as follows.

Tat purushaaya vidmahe Vakratundaaya dheemahi  Tanno dhanti prachodayaat.

He has as his vehicle as small mouse. He is the presiding Deity of the Muladhara Chakra, the psychic centre in the body in which the Kundalini Shakti resides.

His Bija Akshara (root syllable) is Gung, pronounced to rhyme with the English word "sung". He is the Lord of harmony and peace.

Lord Ganesh represents AUM or the Pranava, which is the chief Mantra among the Hindus. Nothing can be done without uttering it. This explains the practice of invoking Ganesh before beginning any rite or undertaking any project. His two feet represent the power of knowledge and the power of action. The elephant head is significant in that it is the only figure in nature that has the form of the symbol for AUM.

The significance of riding on a mouse is the complete conquest over egoism. The holding of the ankusha represents His rulership of the world. It is the emblem of divine Royalty.

Riding on a mouse, one of nature's smallest creatures and having the head of an elephant, the biggest of all animals, denotes that Ganesh is the creator of all creatures.

Elephants are very wise animals; this indicates that Lord Ganesh is an embodiment of wisdom. It also denotes the process of evolution--the mouse gradually evolves into an elephant and finally becomes a man. This is why Ganesh has a human body, an elephant's head and a mouse as His vehicle. This is the symbolic philosophy of His form.

He is the Lord of Gunas or groups, for instance groups of elements, groups of senses, etc. He is the head of the followers of Shiva or the celestial servants of Lord Shiva. Lord Ganesh's two powers are the Kundalini and the Vallabha or power of love.

He carries a Modak (sweet dumpling) in one hand, for his appetite is insatiable, and conscious of his role the other hand shows in the 'abhaya mudra' (do not fear, I am here to protect).