Taking your questions one at a time:
How should you refer to the entity group in the software? Hard-code the id, or the name?
Refer to the entity groups in a way that makes your code the most readable. So, perhaps you use the name, or perhaps a constant that looks like the name but whose value is the id. Using a constant can avoid one join when you are looking up entities by group type, but usually this is not much of a concern.
Why do I even need that table in the DB then? Is this the wrong way to structure my data?
This is a perfectly acceptable way to structure your data. The most correct way depends on what you are doing with the data, but for most applications your structure would be correct. However, you certainly don't need that table in the database--you could instead have a "group_type" field on the entity_group table. Here are the pros and cons:
Advantages of the current structure:
- Easy to add fields that describe the entity_group_type. For example, you might want to make some group types only viewable by admin users, or disabled, or whatever. If this is a possiblity for the future, it pretty much requires this database structure.
- Ability to have your database software enforce referential integrity, meaning the data is kept consistent between the entity_group and entity_group_type tables.
Advantages of adding a group_type field on the entity_group table:
- Possibly a simpler representation in your code. For exameple, if you use a MVC architecture, having the extra table might require another model object in your code. That's usually not a problem, and may have advantages, but sometimes simpler is better.
- When you are looking up entities by entity group type, your SQL statements will be slightly simpler, since there will be one less table/join involved.
I think in most cases your current structure comes out ahead, although it does depend of how you use the data. Unless you had a good reason to structure the data differently, I would stick with your current structure.