By default Kentico doesn't allow to change Form Code Name and Table Name. I would emphasize that it is not a good practice to amend the objects in database directly. Maybe you will be ok with just changing Display Name instead, please consider this option. Or create a new Form object instead with a proper name (this would be the best option).
But if you're sure in what are you doing these are the tasks (as per my knowledge, there might be more). As an example I will be using "Contact Us" form from Dancing Goat MVC test site:
- Perform a database backup
- Rename the Form_DancingGoatMvc_ContactUsNew database table
- Amend the CMS_Form record (change FormName) of Contact Us form
- Check and amend the CMS_Class record (check and change ClassName, ClassXmlSchema, ClassFormDefinition, ClassTableName if needed)
- Restart the website, regenerate the form code in Forms application (if you are using it) and update the form generated code in your solution
If you also want to change ID column name please check all the columns in CMS_Class table, there might be more references to ID column name.