First of all you need to remove the data from the device - look up and perform master reset for your model in the respective user manual. That's the first thing to do when you purchase a second hand device (and before you sell it again).
Then, if the account is new, just abandon it, and start a new one. If it is already na older account, and you do not want to abandon it, then you can delete individual activites in Garmin Connect, you can adjust your personal data (HR zones, weight, heigth,...), but you wan't be able to delete things like Steps, Calories, etc.
