Modern browsers have Array#includes, which does exactly that and is widely supported by everyone except IE:

console.log(['joe', 'jane', 'mary'].includes('jane')); // true

You can also use Array#indexOf, which is less direct, but doesn't require polyfills for outdated browsers.

console.log(['joe', 'jane', 'mary'].indexOf('jane') >= 0); // true

Many frameworks also offer similar methods:

• jQuery: $.inArray(value, array, [fromIndex])
• Underscore.js: _.contains(array, value) (also aliased as _.include and _.includes)
• Dojo Toolkit: dojo.indexOf(array, value, [fromIndex, findLast])
• Prototype: array.indexOf(value)
• MooTools: array.indexOf(value)
• MochiKit: findValue(array, value)
• MS Ajax: array.indexOf(value)
• Ext: Ext.Array.contains(array, value)
• Lodash: _.includes(array, value, [from]) (is _.contains prior 4.0.0)
• Ramda: R.includes(value, array)

Notice that some frameworks implement this as a function, while others add the function to the array prototype.

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
}

Instead of using an API that is currently marked as "experimental" consider using a more broadly supported method, such as Array.prototype.indexOf() (which is also supported by IE).

Instead of t.title.includes(string) you could use t.title.indexOf(string) >= 0

You can also use Array.prototype.filter() to get a new array of strings that meet a certain criteria, as in the example below.

var arr = ["one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten"];
document.getElementById("input").onkeyup = function() {
  document.getElementById("output").innerHTML = arrayContainsString(arr,this.value);
}
document.getElementById("header").innerHTML = JSON.stringify(arr);

function arrayContainsString(array, string) {
  var newArr = array.filter(function(el) {
    return el.indexOf(string) >= 0;
  });
  return newArr.length > 0;
}

<input id="input" type="text" />
<br/>
<div>array contains text:<span id="output" />
</div>
<div id="header"></div>

Array.includes compares by object identity just like obj === obj2, so sadly this doesn't work unless the two items are references to the same object. You can often use Array.prototype.some() instead which takes a function:

const arr = [{a: 'b'}]
console.log(arr.some(item => item.a === 'b'))

But of course you then need to write a small function that defines what you mean by equality.