groups.js

// Inputs: List of names
// Outputs: Groups of size 3-5, randomized

// Pseudocode:
// Take array of names
// Shuffle this array
// Split into groups
// Check if length is less than 3
    // Return randomized list
// Split shuffled array into groups of 3-5
// Return an array of arrays (each with group of people)

const shuffle = (array) => {
    const shuffledArray = array.slice()

    for (let i = (shuffledArray.length - 1); i >= 0; i--) {
        const randomIndex = Math.floor(Math.random() * i)
        const temp = shuffledArray[randomIndex]
        shuffledArray[randomIndex] = shuffledArray[i]
        shuffledArray[i] = temp
    }

    return shuffledArray
}

const randomGroups = (names, minSize = 3) => {
    const shuffledNames = shuffle(names)

    if (names.length <= minSize) {
        return shuffledNames
    } else {
        const allGroups = []
        let tempGroup = []

        for (let i = 0; i < names.length; i++) {
            if (tempGroup.length < minSize) {
                tempGroup.push(shuffledNames[i])
            } else {
                allGroups.push(tempGroup)
                tempGroup = [shuffledNames[i]]
            }
        }

        let remainder = names.length % minSize

        for (let i = 0; i < remainder; i++) {
            allGroups[allGroups.length - 1].push(shuffledNames.pop())
        }

        return allGroups
    }
}

const letters = 'abcdefghijklmnopqrstuvwxyz'.split('')

console.log(randomGroups(letters))

See revisions for previous version before refactoring!