Both names translate to "cowherd". Sanskrit go means "cow"; pāla and vinda form tatpurusha compounds, literally translating to "finder of cows" and "protector of cows", respectively.
The story of how Krishna was given the name Govinda is described in detail in the Vishnu Purana. After lifting Govardhan hill to protect the villagers and cows of Vrindavan, the lord of devas Indra awarded him the title.
A famous prayer called the Bhaja Govindam was composed by Adi Sankara, a summary of which is; "If one just worships Govinda, one can easily cross this great ocean of birth and death." This refers to the belief that worshipful adoration of Krishna can lead believers out of the cycle of reincarnation, or samsara, and into an eternal blissful life in Vaikuntha, 'beyond this material world' where Govinda resides.
Govinda is a name of Krishna and also appears as the 187th and 539th names in the Vishnu Sahasranama.
According to Adi Sankara's commentary on the Vishnu Sahasranama, translated by Swami Tapasyananda, Govinda has three meanings:
In the Harivamsa, Indra praised Krishna for having attained loving leadership of the cows which Krishna tended as a cowherd, by saying, "So men too shall praise Him as Govinda."
According to Klaus Klostermaier, Krishna Gopijanavallabha, Krishna the lover of the Gopis, is the latest stage in the historical process resulting in contemporary Krishnaism, being added to the worship of Bala Krishna (the Divine Child Krishna), and the original cult of Krishna-Vasudeva which may date back to several centuries before the Common Era.