Use regex.test() if all you want is a boolean result:

console.log(/^([a-z0-9]{5,})$/.test('abc1')); // false

console.log(/^([a-z0-9]{5,})$/.test('abc12')); // true

console.log(/^([a-z0-9]{5,})$/.test('abc123')); // true

...and you could remove the () from your regexp since you've no need for a capture.

You can use a string as a regular expression using the RegExp Object:

var myPattern = new RegExp('.'+myWord,'g'); 

Fiddle Example

Doing a single match in your case, is simply changed the second parameter in RegExp from g to m (which means to make one match per line for multi lines, but in this case a strings is simply all one line). For finding the word "wood" from "ood","od","d", or other cases. You can do this:

var myPattern = new RegExp("\\b\\w+"+myWord+"\\b",'m'); 

Note I have a solution in the comments below, but this one is better.

The items \\b ... \\b mean word boundaries. Basically ensuring that it matches a single word. Then the \\w means any valid "word character". So overall the regexp means (using myWord = "od"):

|word boundary| + (1 or more word characters) + "od" + |word boundary|

This will ensure that it matches any words in the string than end with the characters "od". Or in a more general case you can do:

var myPattern = new RegExp("\\b\\w*"+myWord+"\\w*\\b",'m'); 

Use the regex constructor, like:

function myFunction() {
    var str = "The rain in SPAIN stays mainly in the plain",
        test = "ain",
        re = new RegExp(test, 'gi'),
        res = str.match(re);

    console.log(res);
}

Global Variable Scope

It is because you are using name as your variable. This is a global browser window variable that is inherently a string and cannot be stored as an Array

Even if you redeclare it with var name =, you are still in the global scope. And thus name (aka window.name) simply retains the last value you assign to it.

You can test this with the following on an empty page without defining any variables at all:

console.log(name===window.name) // Returns true
console.log(name,window.name)   // Returns 'Safari Safari' for my browser

Change name to something else

If you change your name variable to simply have a different name, like my_name, it stores the result of .match() as an Array.

var my_name = str.match(/[^\/]+/i);
var version = str.match(/[0-9|\.]+/i);

console.log(typeof my_name, my_name instanceof Array) // Returns object, true

Change Scope by wrapping in a function

This is your exact code wrapped inside a function and returns the correct variable types:

function getBrowserStuff(){

    var userAgent = navigator.userAgent;
    var splitted = userAgent.match(/[(][^)]+[)]|\w+\/\S+/ig);

    for (var i = 0; i < splitted.length; i++ ) {
        var str = splitted[i];
        if (str[0] == '(') {
        } else {
            var name = str.match(/[^\/]+/i);
            var version = str.match(/[0-9|\.]+/i);
            console.log('Name','Typeof '+(typeof name), 'IsArray '+(name instanceof Array),name)
            console.log('Version','Typeof '+(typeof version),'IsArray '+(version instanceof Array),version)
        }
    }

    return 'whatever'
}

getBrowserStuff()

Changing the variable name to my_name OR wrapping code like the above function returns this:

Name    Typeof object IsArray true ["Mozilla"]
Version Typeof object IsArray true ["5.0"]
Name    Typeof object IsArray true ["AppleWebKit"]
Version Typeof object IsArray true ["600.3.18"]
Name    Typeof object IsArray true ["Version"]
Version Typeof object IsArray true ["8.0.3"]
Name    Typeof object IsArray true ["Safari"]
Version Typeof object IsArray true ["600.3.18"]

Where before it returned this:

Name    Typeof string IsArray false Mozilla
Version Typeof object IsArray true  ["5.0"]
Name    Typeof string IsArray false AppleWebKit
Version Typeof object IsArray true  ["600.3.18"]
Name    Typeof string IsArray false Version
Version Typeof object IsArray true  ["8.0.3"]
Name    Typeof string IsArray false Safari
Version Typeof object IsArray true  ["600.3.18"]