No, there is no as such drawback using the same names for both bands.But device which are close to the router will have a good network and the devices which are far will face bad network.
May be ,you may face some connectivity and speed related issues by using the same WiFi name for both bands.
Yes , you might face the connectivity issue or speed issue .
Yes, you might face issues related to the connectivity or speed into the home network
Yes, sometime you can get connectivity or the speed-related issues.
If you use the same WiFi name for both the Band in Dual-band router then you might get the connectivity issue and the Internet Speed related issue.