Is there a way to have the label changes appear on the Activity Log?

Buenas @Tricia Tuanquin @Rasmus Wulff Jensen @Mike - Dreamsuite Consulting 

For me, the best way to solve this "shortcoming" of Trello is the following automation.

Every time a user adds a tag with a specific name, a comment will be added to the card with the name of the person who added it and the text I indicated in the image.

The {username} and {labelname} variables are great for this type of automation. Unfortunately, you can't use the {labelname} variable in the action trigger, which would increase the power of this automation by avoiding having to create a separate automation for each tag. At least I didn't know how to do it.

You can configure the trigger with many specifications or restrictions to suit your taste.
I hope this helps.
Best regards

Not inside Trello, but this tool can tell you when changes to Labels where made: https://trellotools.azurewebsites.net/CardHistory (in the past it could also tell if it was an was an add/update/delete of labels but a current bug in Trello right now make that impossible :-( [Go here to vote for getting it Fixed: https://jira.atlassian.com/browse/TRELLO-1254]

Okay, I just discovered that you can activate the "any" option on the trigger... It was pretty obvious haha

Hi @Tricia Tuanquin , its not a perfect solution but it can be implemented now...

You can create an automation to do this....