user14524: I want to know the names of the variations in the Ruy Lopez Chigorin, for example:
[FEN ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3 Na5 10.Bc2 c5 11.d4 Nd7

I look at the opening classification on Chessbase but it's not very detailed with names. Also chess365.com. 
Is there anywhere else I can see names of variations?

user14526: I use Arena, a chess software with stockfish engine downloaded to it. So what you can do is play the variation on both sides and it will show you the name of the variation

user14532: Not especially - see for instance the discussion at What are all the most common transpositions between the Caro-Kann Panov–Botvinnik Attack with 5...e6 6. Nf3 Bb4 and the Nimzo-Indian Defence?

d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. e3 O-O 5. Bd3 d5 6. Nf3 c5 7. O-O cxd4 8. exd4 dxc4 9. Bxc4 

or

e4 c6 2. d4 d5 3. exd5 cxd5 4. c4 Nf6 5. Nc3 e6 6. Nf3 Bb4 7. Bd3 dxc4 8. Bxc4 O-O 9. O-O

both end up with the same position but argually one will be tagged as a Caro-Kann and one as a Nimzo-Indian.

user14463: You can go to Lichess.org and in  toolbar in the top choose Tools. In that page there is a small icon which looks like book. You can chose which opening book you want to look up either the GM games or online games. The variation names are written there.
The game you mentioned is 'C90 Ruy Lopez closed variation, closed defense' up to move 9. In the first move of white in move 9 it goes out of the opening book.

user12951: My free, open-source software, pgn-extract, provides a file eco.pgn that provides names for ECO codes. This file can be used with pgn-extract to add ECO tags to game scores: see its -e flag. For instance, the tags it produces for the moves: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 Be7 6.Re1 b5 7.Bb3 d6 8.c3 0-0 9.h3 Na5 10.Bc2 c5 11.d4 Nd7 * are: 
[ECO "C96"]
[Opening "Ruy Lopez"]
[Variation "closed, Keres (...Nd7) defence"]

That might provides some degree of what you are looking for.

14524: <p>I want to know the names of the variations in the Ruy Lopez Chigorin, for example:</p>

<pre><code>[FEN ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3 Na5 10.Bc2 c5 11.d4 Nd7
</code></pre>

<p>I look at the opening classification on <a href="http://www.chessbase.com" rel="nofollow noreferrer">Chessbase</a> but it's not very detailed with names. Also <a href="https://www.365chess.com/" rel="nofollow noreferrer">chess365.com</a>. </p>

<p>Is there anywhere else I can see names of variations?</p>
 14526: <p>I use Arena, a chess software with stockfish engine downloaded to it. So what you can do is play the variation on both sides and it will show you the name of the variation</p>
 14532: <p>Not especially - see for instance the discussion at <a href="https://chess.stackexchange.com/questions/9461/what-are-all-the-most-common-transpositions-between-the-caro-kann-panov-botvinni">What are all the most common transpositions between the Caro-Kann Panov–Botvinnik Attack with 5...e6 6. Nf3 Bb4 and the Nimzo-Indian Defence?</a></p>

<ol>
<li>d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. e3 O-O 5. Bd3 d5 6. Nf3 c5 7. O-O cxd4 8. exd4 dxc4 9. Bxc4 </li>
</ol>

<p>or</p>

<ol>
<li>e4 c6 2. d4 d5 3. exd5 cxd5 4. c4 Nf6 5. Nc3 e6 6. Nf3 Bb4 7. Bd3 dxc4 8. Bxc4 O-O 9. O-O</li>
</ol>

<p>both end up with the same position but argually one will be tagged as a Caro-Kann and one as a Nimzo-Indian.</p>
 14463: <p>You can go to <a href="http://Lichess.org" rel="nofollow noreferrer">Lichess.org</a> and in  toolbar in the top choose Tools. In that page there is a small icon which looks like book. You can chose which opening book you want to look up either the GM games or online games. The variation names are written there.</p>

<p>The game you mentioned is 'C90 Ruy Lopez closed variation, closed defense' up to move 9. In the first move of white in move 9 it goes out of the opening book.</p>
 12951: <p>My free, open-source software, <a href="https://www.cs.kent.ac.uk/people/staff/djb/pgn-extract/" rel="nofollow noreferrer">pgn-extract</a>, provides a file eco.pgn that provides names for ECO codes. This file can be used with pgn-extract to add ECO tags to game scores: see its -e flag. For instance, the tags it produces for the moves: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 Be7 6.Re1 b5 7.Bb3 d6 8.c3 0-0 9.h3 Na5 10.Bc2 c5 11.d4 Nd7 * are: </p>

<pre><code>[ECO "C96"]
[Opening "Ruy Lopez"]
[Variation "closed, Keres (...Nd7) defence"]
</code></pre>

<p>That might provides some degree of what you are looking for.</p>
