Application Insights Dependency types

There's no limitation that I'm aware of.
Some dependencies are reported automatically by the SDK (such as SQL, Ajax), so these will get a pretty name in Application Map, but you can put there whatever makes sense in your application's BL.
The list of out-of-the-box dependency types Application Insights collect right now can be found here, although the documentation does not contain the dependency type string that you're interested in.
Non definitive list from my own experience:

• SQL
• HTTP
• Azure queue
• Azure table
• Azure blob
• Azure DocumentDb
• Ajax
• Redis
• Azure Service Bus
• MySQL
• Azure IoT Hub
• Azure Event Hubs

The are dependency types getting custom icons in Application Map:
- SQL
- Custom HTTP types, based on the following criteria:
1. Azure blob: when host name ends with blob.core.windows.net
2. Azure table: when host name ends with table.core.windows.net
3. Azure queue: when host name ends with queue.core.windows.net
4. Web Service: when host name ends with .asmx or contains .asmx/
5. WCF Service: when host name ends with .svc or contains .svc/
- All other HTTP or AJAX

Going forward the list will be extended with other dependency types that will get custom item in ApplicationMap.