What song is playing?

Retina, 242

Try it online!

iG`^na( na)*$
iM`na
m`^8$
>Batman Theme,Neal Hefti$n>Na Na Hey Hey Kiss Him Goodbye,Steam
m`^10$
>Katamari Damacy,Yuu Miyake
m`^11$
>Hey Jude,The Beatles
[0-9].+
>Land Of 1000 Dances,Wilson Pickett
m`^[0-9]
>Africa,Toto
>
Song: 
,
$nArtist: 

How it works:

IgnoreCase flag + Grep mode flag + Regex ^na( na)*$. If the input is valid, print it as is. If not, print nothing.

iG`^na( na)*$

IgnoreCase flag + Match mode flag + Regex na. Count the "na"s and print the number.

iM`na

If the string is exactly "8", replace by the second line.

m`^8$
>Batman Theme,Neal Hefti$n>Na Na Hey Hey Kiss Him Goodbye,Steam

If the string is exactly "10", replace by the second line.

m`^10$
>Katamari Damacy,Yuu Miyake

If the string is exactly "11", replace by the second line.

m`^11$
>Hey Jude,The Beatles

If the string matches [0-9].+, replace by the second line. This is neither true for single digit numbers, 10 and 11 as they already have been repaced nor any of the above replacement strings.

[0-9].+
>Land Of 1000 Dances,Wilson Pickett

If none of the above matched, the string still starts with a number. Default to Toto, Africa.

m`^[0-9]
>Africa,Toto

Replace the placeholders > and , by Song: and Artist:.

>
Song: 
,
$nArtist: 

JavaScript (ES6), 276 bytes

alert(`Song: `+([,`Batman Theme,Neal Hefti
Song: Na Na Hey Hey Kiss Him Goodbye,Steam`,,`Katamari Damacy,Yuu Miyake`,`Hey Jude,The Beatles`,`Land Of 1000 Dances,Wilson Pickett`][+prompt(i=0).replace(/na( |$)/gi,_=>++i)&&(i>11?4:i-7)]||`Africa,Toto`).replace(/,/g,`
Artist: `))

Explanation

Input can optionally contain one trailing space.

alert(                 // output the result
  `Song: `+([          // insert the "Song:" label
      ,                // set the first element to undefined in case input is empty

      // Songs
      `Batman Theme,Neal Hefti
Song: Na Na Hey Hey Kiss Him Goodbye,Steam`,
      ,
      `Katamari Damacy,Yuu Miyake`,
      `Hey Jude,The Beatles`,
      `Land Of 1000 Dances,Wilson Pickett`

    ][
      +                // if the input string was made up only of "na"s, the replace would
                       //     return a string containing only digits, making this return a
                       //     number (true), but if not, this would return NaN (false)
        prompt(        // get the input string
          i=0          // i = number of "na"s in input string
        ).replace(     // replace each "na" with a number
          /na( |$)/gi, // find each "na"
          _=>++i       // keep count of the "na"s and replace with a (non-zero) number
        )
      &&(i>11?4:i-7)   // select the song based on the number of "na"s
    ]
      ||`Africa,Toto`  // default to Africa
  ).replace(/,/g,`
Artist: `)             // insert the "Artist:" label
)

Test

var prompt = () => input.value;
var alert = (text) => result.textContent = text;
var solution = () => {

alert(`Song: `+([,`Batman Theme,Neal Hefti
Song: Na Na Hey Hey Kiss Him Goodbye,Steam`,,`Katamari Damacy,Yuu Miyake`,`Hey Jude,The Beatles`,`Land Of 1000 Dances,Wilson Pickett`][+prompt(i=0).replace(/na( |$)/gi,_=>++i)&&(i>11?4:i-7)]||`Africa,Toto`).replace(/,/g,`
Artist: `))

}

<input type="text" id="input" value="na na Na na NA na na nA" />
<button onclick="solution()">Go</button>
<pre id="result"></pre>

PowerShell, 278 bytes

• Can handle any amount of whitespace
• No regex whatsoever!
• Implicit typecasting FTW!

@{8='Batman Theme/Neal Hefti','Na Na Hey Hey Kiss Him Goodbye/Steam'
10='Katamari Damacy/Yuu Miyake'
11='Hey Jude/The Beatles'
12='Land Of 1000 Dances/Wilson Pickett'}[[math]::Min($args.Count*!($args|?{$_-ne'na'}),12)]|%{'Song: {0}
Artist: {1}'-f($_+'Africa/Toto'*!$_-split'/')}

Ungolfed

@{8='Batman Theme/Neal Hefti','Na Na Hey Hey Kiss Him Goodbye/Steam' # array
10='Katamari Damacy/Yuu Miyake'
11='Hey Jude/The Beatles'
12='Land Of 1000 Dances/Wilson Pickett'} # Hashtable of songs
[   # Get value by key from hashtable
    # If key is invalid, silently return null value

    [math]::Min( # Clamp max value to 12
        $args.Count* # Multiply count of argumens
                     # true/false will be cast to 1/0
            ! # Negate result of expression
              # Will cast empty array to 'false'
              # and non-empty array to 'true'
            (
                # Return non-empty array if input arguments
                # contain anything other than 'na'
                $args | Where-Object {$_ -ne 'na'} 
            ),
        12
    )
] | ForEach-Object { # Send value from hashtable down the pipeline,
                     # This allows to process arrays in hasthable values
    'Song: {0}
    Artist: {1}' -f ( # Format string
        $_+ # Add to current pipeline variable
            'Africa/Toto'*!$_ # If pipeline variable is empty,
                              # then add default song to it
                              # Example: 'Test'*1 = 'Test'
                              #          'Test'*0 = null
        -split '/' # Split string to array for Format operator
    )
}

Usage

PS > .\WhatSong.ps1 na na na na na na na na
Song: Batman Theme
Artist: Neal Hefti
Song: Na Na Hey Hey Kiss Him Goodbye
Artist: Steam

PS > .\WhatSong.ps1 Na na na na na na na na na Na
Song: Katamari Damacy
Artist: Yuu Miyake

PS > .\WhatSong.ps1 Na na na na na na na na na BanaNa
Song: Africa
Artist: Toto