Can cellular network providers detect the phone model/make when their sim is activated? When the user inserts the sim card and activates, can the cellular network provider detect what phone the user uses?

Like say Motorola Droid. 

Or at least the phone is a smartphone or not?
The amount of information your carrier knows about you can be scary What Your Wireless Carrier Knows About You covers this in  detail. To answer your question specifically, quoting from this:



In general terms, wireless operators capture three main kinds of information: information about the devices connected to the network, metadata about the packets of data that run through the network, and information about the content contained in the packets being downloaded or uploaded by the subscriber.

If they (carriers) wanted to, these engineers (network engineers ) could detect a single device entering a specific cell and identify the type of device it is, its operating system (if it’s a smartphone, a tablet, or a laptop USB modem), its IP address, its bandwidth consumption, and even the apps it is running.

Wireless operators need to know about the devices on their network so that they can make assumptions about the sorts of content their customers are using and the amount of bandwidth they’ll need. For example, if the carrier knows that the smartphones it has detected typically have large screens, it can conclude that those devices will probably be consuming a relatively large amount of streaming video content, which requires a lot of bandwidth.

Similarly, carriers can detect smaller, less expensive phones that don’t run a real OS but do sport a full keyboard. The operator can deduce that these devices are specialized for social networking, which doesn't demand a lot of bandwidth but does require a lot of signaling in the network.




This post What does your mobile carrier know about you? quotes a 2010 justice department memo and provides a link to retention period of such information by various carriers in USA


As revealed in the memo, mobile carriers capture a variety of data about you, including call detail records (who you called and when), text message details (who you texted and when), text message content, bill copies, payment history, and even which cell towers you use. Another category, called Subscriber Information, presumably tracks your name and all necessary contact details.


https://security.stackexchange.com/questions/71795/is-my-phone-carrier-monitoring-my-traffic provides related information