Another poossible solution is based on the array_search() function. You need to use PHP 5.5.0 or higher.

Example

$userdb=Array
(
    0 => Array
        (
            "uid" => '100',
            "name" => 'Sandra Shush',
            "url" => 'urlof100'
        ),

    1 => Array
        (
            "uid" => '5465',
            "name" => 'Stefanie Mcmohn',
            "pic_square" => 'urlof100'
        ),

    2 => Array
        (
            "uid" => '40489',
            "name" => 'Michael',
            "pic_square" => 'urlof40489'
        )
);

$key = array_search(40489, array_column($userdb, 'uid'));

echo ("The key is: ".$key);
//This will output- The key is: 2

Explanation

Summary

array_search('breville-one-touch-tea-maker-BTM800XL', array_column($products, 'slug'));

or, if you prefer:

// define function
function array_search_multidim($array, $column, $key){
    return (array_search($key, array_column($array, $column)));
}

// use it
array_search_multidim($products, 'slug', 'breville-one-touch-tea-maker-BTM800XL');

The original example(by xfoxawy) can be found on the DOCS.
The array_column() page.

Update

Due to Vael comment I was curious, so I made a simple test to meassure the performance of the method that uses array_search and the method proposed on the accepted answer.

I created an array which contained 1000 arrays, the structure was like this (all data was randomized):

[
      {
            "_id": "57fe684fb22a07039b3f196c",
            "index": 0,
            "guid": "98dd3515-3f1e-4b89-8bb9-103b0d67e613",
            "isActive": true,
            "balance": "$2,372.04",
            "picture": "http://placehold.it/32x32",
            "age": 21,
            "eyeColor": "blue",
            "name": "Green",
            "company": "MIXERS"
      },...
]

I ran the search test 100 times searching for different values for the name field, and then I calculated the mean time in milliseconds. Here you can see an example.

Results were that the method proposed on this answer needed about 2E-7 to find the value, while the accepted answer method needed about 8E-7.

Like I said before both times are pretty aceptable for an application using an array with this size. If the size grows a lot, let's say 1M elements, then this little difference will be increased too.

Update II

I've added a test for the method based in array_walk_recursive which was mentionend on some of the answers here. The result got is the correct one. And if we focus on the performance, its a bit worse than the others examined on the test. In the test, you can see that is about 10 times slower than the method based on array_search. Again, this isn't a very relevant difference for the most of the applications.

Update III

Thanks to @mickmackusa for spotting several limitations on this method:

• This method will fail on associative keys.
• This method will only work on indexed subarrays (starting from 0 and have consecutively ascending keys).

Note on Update III

• not taking performance into account: you can use array_combine with array_keys & array_column to overcome this limitation in a one-liner like:

$product_search_index = 
array_search( 'breville-one-touch-tea-maker-BTM800XL', array_filter( array_combine( array_keys($products), array_column( $products, 'slug' ) ) ) );

Just for fun, if the array is 0 based and sequential keys:

echo array_search('zero', array_column(json_decode($json, true), 'name'));

• Extract all the name key values into a single array
• Search for the name value to return the key

This decodes the JSON into an array. You can decode it to an object after if you need that. As of PHP 7 you can use an array of objects:

echo array_search('zero', array_column(json_decode($json), 'name'));