Can you link to your codepen?

Link: https://codepen.io/Leinad-Noscaj/pen/RNNbZqQ

You should see error:

SyntaxError: missing } after property list 
 at https://cdpn.io/cpe/boomboom/index.html?editors=1111&key=index.html-92ce83c4-3f00-ca09-07a4-bcb8925ee348:136

Go to the URL in the error so you can see just the resulting page without the codepen junk wrapping it. Look in the browser console (F12) and you'll see (in Firefox):

Uncaught SyntaxError: missing } after property list    index.html:136:13
note: { opened at line 119, column 63    index.html:119:63

Those will have links you can click and it'll show you exactly the line with the problem: Line 107 is });, needs to be }});.

   success: function (player) {
      player.animationState.setAnimation(0, "first animation name", true);
      player.animationState.addAnimation(0, "second animation name", true, 3);
   }

What do you mean by "trigger"? That isn't a verb usually used for tracks.

If you want to play two animations at the same time:

   success: function (player) {
      player.animationState.setAnimation(0, "lower track animation name", true);
      player.animationState.setAnimation(1, "higher track animation name", true);
   }

Yep, add animation queues the animation for playback after the current or last queued animation.

What are you trying to accomplish with trackEnd? It's almost never what you want. Use an empty animation instead:
https://esotericsoftware.com/spine-applying-animations#Empty-animations

The 3 I gave above for addAnimation is your 3 second delay. See:
https://esotericsoftware.com/spine-api-reference#AnimationState-addAnimation2

If you set the delay parameter to 0 it'll use the duration of the first animation.

setAnimation takes 3 parameters, not 4:

player.animationState.setAnimation(0, "run", true, 5);

addAnimation takes 4 parameters, not 3:

player.animationState.addAnimation(0, "jump", false); // Missing the delay param.

Make sure you understand the parameters (read the docs).

The true being passed makes that animation loop if playback exceeds the animation duration. If false is passed it will give you the last frame forever.

It's easy to play a single animation looping forever. To play multiple animations repeatedly, you'll need a listener to know when they are done, then you set the animations again:

success: function (player) {
	var loop = function () {
		player.animationState.addAnimation(0, "jump", true, 0);
		var entry = player.animationState.addAnimation(0, "run", true, 3);
		entry.listener = {
			complete: function (event) {
				loop();
			}
		};		 
	};
	loop();
},

There are other events available beside complete, see the API reference docs.

You can also mix between animations, so the change is not so abrupt:

player.animationState.data.defaultMix = 0.2;
player.animationState.addAnimation(0, "jump", true, 0);

Or on a specific transition:

var entry = player.animationState.addAnimation(0, "jump", true, 0);
entry.mixDuration = 0.2;

As an example of some advanced usage, here are some pages using spine-player and the code for them:
https://esotericsoftware.com/blog/Spine-4.0-is-here
http://esotericsoftware.com/files/blog/4.0-released/blog.js

And:
https://esotericsoftware.com/blog/Spine-4.2-The-physics-revolution
https://esotericsoftware.com/files/blog/4.2-released/blog.js

You're welcome!

"skin" means something else in Spine. I assume you mean different skeletons may not have some animations. To set an animation only if it exists:

var animation = player.skeleton.data.findAnimation("run");
if (animation) player.animationState.addAnimation(0, animation, true, 0);

What do you mean by "define a constant inside an animation name"?

I'm not sure what you are asking. Basic programming maybe?

var name = "something";
var animation = player.skeleton.data.findAnimation(name + "-run");

If that's missing the mark, you'll need to better explain what you are trying to accomplish. Sometimes it's faster if you know exactly what to ask, sometimes you need to lay out the whole situation so we can give the appropriate advice.

If you play A and then queue (using addAnimation, not setAnimation) B using delay 0, the actual delay used will be such that B starts when A ends.

If there is a mix duration from A to B, delay 0 will start B at the A duration minus the mix duration, so when B mixing is done, A has just ended. Eg A is 0.3 duration and mix is 0.2. Queuing B with delay zero would use a delay of (0.3 - 0.2) = 0.1.

Read the API reference and try watching this video, even though it's for Unity it explains AnimationState concepts:

It's JavaScript, so:

var entry = player.animationState.addAnimation(2, "jumpStart", false, 3);
entry.mixDuration = 1;