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Yes, you can create tags from the admin panel of your community, in the "Media tags" tab just clicking on "+Create tag". 

If you want to classify the media content by these tags, go to your profile, to the media content area, and when uploading or editing the media include that tags on the keywords field. 

For more info please follow this link: How do I upload media?

Remember, If you want to share the media from your profile, you have to select the Event or the Community where this media should be available.