In Sanskrit, "Govida" (Govindam) is one of the names given to Sri Krsna. It is a joint name from two words: gov = cows + indam = god.
Govinda was the person who was the god of the cows or the person who took care of the cows, just like the One takes care of man. Cows are very sacred in Bharat (India). They are entitled respect and loyalty, because they are like mothers (read: Holy Cow by Steven J. Rosen)".
(Background Information: "Govinda" is a folk/devotional song and it is about Sri Krsna.)
In Hesse's novel, Gonvida "is Siddhartha's childhood friend and confidant. He loves everything about Siddhartha—his eyes, his voice, the way he walked, his grace. Govinda becomes Siddhartha's shadow. Like Siddhartha, Govinda must also go his own way. Siddhartha supports his friend's decision when Govinda leaves him to follow Gotama Buddha, stating, "Often I have thought: will Govinda ever take a step without me, from his own conviction? Now, you are a man and have chosen your own path."
The friends meet at strategic points in their lives. After Siddhartha has attained eternal bliss, Govinda kisses his forehead, compelled by love and presentiment. It is through this kiss and not through Siddhartha's teaching that Govinda finally attains union with the universal, eternal essence." And, ultimately, victory.
"Govinda" is one of the names of the Supreme Godhead, and, consequently, the name of Krishna in his identity as God.
The name actually is "Govind," the Protector. Govind is the protector and preserver of the universe; he is the source of power.
However, "Gov" means cow. Krishna, in his worldly aspect was the preserver of cows, and so came to be known as Govinda, which also means the protector of cows.
The interconnection of the names and meanings may be better understood by taking the name of "Shepherd" as an analogy. Shepherd means the sheep-herd, the person who herds, and therefore tends to the sheep. Jesus is the Shepherd of Souls, that is he tends to the care of the souls.
As far as the book Siddhartha is concerned, as has already been explained by previous respondents, Govinda is the name of Siddhartha's friend. (No religious significance was meant by Hesse in the choice of that name.)