There isn't any need to reinvent the wheel loop, at least not explicitly.

Use some as it allows the browser to stop as soon as one element is found that matches:

if (vendors.some(e => e.Name === 'Magenic')) {
  // We found at least one object that we're looking for!
}

or the equivalent (in this case) with find, which returns the found object instead of a boolean:

if (vendors.find(e => e.Name === 'Magenic')) {
  // Usually the same result as above, but find returns the element itself
}

If you'd like to get the position of that element, use findIndex:

const i = vendors.findIndex(e => e.Name === 'Magenic');
if (i > -1) {
  // We know that at least 1 object that matches has been found at the index i
}

If you need to get all of the objects that match:

if (vendors.filter(e => e.Name === 'Magenic').length > 0) {
  // The same result as above, but filter returns all objects that match
}

If you need compatibility with really old browsers that don't support arrow functions, then your best bet is:

if (vendors.filter(function(e) { return e.Name === 'Magenic'; }).length > 0) {
  // The same result as above, but filter returns all objects that match and we avoid an arrow function for compatibility
}

If you need to modify the existing Array, you should use splice().

for (var i = array.length - 1; i > -1; i--) {
    if (array[i].name === "zipCode")
        array.splice(i, 1);
}

Notice that I'm looping in reverse. This is in order to deal with the fact that when you do a .splice(i, 1), the array will be reindexed.

If we did a forward loop, we would also need to adjust i whenever we do a .splice() in order to avoid skipping an index.