Here's a possibility building on Silviu's answer. Use the array .find() function to look for possible matches in arr1 that match objects in the merged arrays.
If all objects of arr1 are found in the others, then test is green, else test fails. The following snippet passes for me, however if i was to add {name: "Charlie"} to arr1, we'll then see it start to fail.
test("Check value in array matches any value in other array", () => {
const arr1=[{name:"Alice"},{name:"Bob"}]
const arr2=[{name:"Alice"}]
const arr3=[{name:"Bob"}]
const merged = [...arr2, ...arr3]
checkValuesExistInChildArray(arr1, merged)
})
const checkValuesExistInChildArray = (arr1, otherArrays) => {
arr1.find(o => {
const match = otherArrays.find(otherObject => otherObject.name === o.name)
expect(match).exist
})
}