user9229: (C32 King's Gambit Declined, Falkbeer, 5.de) 1. e4 e5 2. f4 d5 3. exd5 ...
Instead I made the move 3. fxe5
What can this variation can be named as?
 [Fen ""]
 [Event "Let's Play!"]
 [Site " Chess.com"]
 [Date "Jul 1, 2016"]
 [White "anandsadasivam"]
 [Black "MaximusXIV"]
 [Result "1-0"]
 [WhiteElo "1168"]
 [BlackElo "1000"]
 [TimeControl "1 in 14 days"]
 [Termination "anandsadasivam won on time"]
 1. e4 e5 2. f4 d5 3. fxe5  1-0

Wherein the one with ECO code C32 comes up like this
[Fen ""]
1. e4 e5 2. f4 d5 3. exd5 e4 4. d3 Nf6 5. dxe4


user-1: The opening trap doesn't have a name, but was made famous in the game Rigaud vs. Cooper, 1974. Not all motifs and variations have names, but you can make reference to this famous game to name the trap.

user2076: As already said, 3. fxe5 ?? is a terrible blunder after which the computer's evaluation drops from about equal to -5 (in Black's favor).
The correct reply by Black is to play Qh4+:


    [FEN "rnbqkbnr/ppp2ppp/8/3pP3/4P3/8/PPPP2PP/RNBQKBNR b KQkq - 0 3"]

    3... Qh4+ 4. g3 Qxe4+ 5. Qe2 Qxh1



The correct play is 3. exd5 by White, after which, Black has the choice to play the "true" counter gambit, probably unsound, but tricky:


    [FEN "rnbqkbnr/ppp2ppp/8/3pp3/4PP2/8/PPPP2PP/RNBQKBNR w KQkq - 0 3"]

    3. dxe5 e4 4. d3 Nf6



And White can claim a small advantage here.
A safer option for Black is to capture on f4, and you get a balanced game, not really a gambit anymore though !


    [FEN "rnbqkbnr/ppp2ppp/8/3pp3/4PP2/8/PPPP2PP/RNBQKBNR w KQkq - 0 3"]


    3. dxe5 exf4



With a very safe position.
Check this article about the King's gambit for more details about this particular trap, and about the King's gambit in general.

user10867: 1. e4 e5 2. f4 d5 is known as the Falkbeer Countergambit.
However, 3.fxe5?? is not a variation but a blunder. As Wikipedia explains, you will either lose material after  3...Qh4+, 4.g3 Qxe4+ (due to a fork between the King and the Rook), or expose your King to the black pieces after 3...Qh4+,  4.Ke2 Qxe4+ 5.Kf2 Bc5+.
I am not aware of a name for 1. e4 e5 2. f4 d5 3. exd5 e4 4. d3 Nf6 5. dxe4. Not every opening variation has a name. 

9229: <p>(C32 King's Gambit Declined, Falkbeer, 5.de) 1. e4 e5 2. f4 d5 3. exd5 ...</p>

<p>Instead I made the move <strong>3. fxe5</strong></p>

<p>What can this variation can be named as?</p>

<pre><code> [Fen ""]
 [Event "Let's Play!"]
 [Site " Chess.com"]
 [Date "Jul 1, 2016"]
 [White "anandsadasivam"]
 [Black "MaximusXIV"]
 [Result "1-0"]
 [WhiteElo "1168"]
 [BlackElo "1000"]
 [TimeControl "1 in 14 days"]
 [Termination "anandsadasivam won on time"]
 1. e4 e5 2. f4 d5 3. fxe5  1-0
</code></pre>

<p>Wherein the one with ECO code C32 comes up like this</p>

<pre><code>[Fen ""]
1. e4 e5 2. f4 d5 3. exd5 e4 4. d3 Nf6 5. dxe4
</code></pre>
 -1: <p>The opening trap doesn't have a name, but was made famous in the game <strong>Rigaud vs. Cooper, 1974</strong>. Not all motifs and variations have names, but you can make reference to this famous game to name the trap.</p>
 2076: <p>As already said, 3. fxe5 ?? is a terrible blunder after which the computer's evaluation drops from about equal to -5 (in Black's favor).
The correct reply by Black is to play Qh4+:</p>

<pre>
<code>
    [FEN "rnbqkbnr/ppp2ppp/8/3pP3/4P3/8/PPPP2PP/RNBQKBNR b KQkq - 0 3"]

    3... Qh4+ 4. g3 Qxe4+ 5. Qe2 Qxh1

</code>
</pre>

<p>The correct play is 3. exd5 by White, after which, Black has the choice to play the "true" counter gambit, probably unsound, but tricky:</p>

<pre>
<code>
    [FEN "rnbqkbnr/ppp2ppp/8/3pp3/4PP2/8/PPPP2PP/RNBQKBNR w KQkq - 0 3"]

    3. dxe5 e4 4. d3 Nf6

</code>
</pre>

<p>And White can claim a small advantage here.
A safer option for Black is to capture on f4, and you get a balanced game, not really a gambit anymore though !</p>

<pre>
<code>
    [FEN "rnbqkbnr/ppp2ppp/8/3pp3/4PP2/8/PPPP2PP/RNBQKBNR w KQkq - 0 3"]


    3. dxe5 exf4

</code>
</pre>

<p>With a very safe position.</p>

<p>Check <a href="https://pawnbreak.com/getting-started-with-the-kings-gambit/" rel="nofollow noreferrer">this article about the King's gambit</a> for more details about this particular trap, and about the King's gambit in general.</p>
 10867: <p><code>1. e4 e5 2. f4 d5</code> is known as the <strong>Falkbeer Countergambit</strong>.</p>

<p>However, 3.fxe5?? is not a variation but a blunder. As <a href="https://en.wikipedia.org/wiki/King&#39;s_Gambit,_Falkbeer_Countergambit" rel="noreferrer">Wikipedia</a> explains, you will either lose material after  3...Qh4+, 4.g3 Qxe4+ (due to a fork between the King and the Rook), or expose your King to the black pieces after 3...Qh4+,  4.Ke2 Qxe4+ 5.Kf2 Bc5+.</p>

<p>I am not aware of a name for 1. e4 e5 2. f4 d5 3. exd5 e4 4. d3 Nf6 5. dxe4. Not every opening variation has a name. </p>
