JIRA is able to have Issue Types with the same name. This is reproduceable:

1. Create a new Sub-Tasks type via Administration > Global Settings > Sub-Tasks. Please refer to Step1.png
2. Go to Administration > Issue Settings > Issue Types, the newly created Sub-Task issue is shown as in screenshot Step1A.png.
3. still in the same page, create a new "Standard Issue Type" with the same name. It is created successfully. Please refer to screenshot Step2.png

This is not re-produceable if Standard Issue Type is created first via Administration > Issue Settings > Issue Types.