I think it is a place to show the issues I created, Like This Issue.
"My issues" is implemented to return the issues that are assigned to you, not reported by you. The idea behind that is that those are the issues that you need to work on and so deserve the most attention.
If you want to find issues based on other, custom criteria, you can use "Advanced search".
Maybe here is a category to be necessary. like "Assigned Issues" category.
Not sure I understand. "My issues" is exactly that. Are you suggesting renaming "My issues" to "Assigned issues"?
The watching category doesn't necessary to show my issues.