I have iMessages on my mac desktop but I can't get text messages on my mac desktop

You need to set your iPhone to forward text messages to your Mac.

On your iPhone:

1. Open Settings
2. Scroll down and tap Messages
3. Tap Text Message Forwarding
4. Turn on the setting for your Mac

To show people's names you need to have your Contacts synched under the same Apple ID on both your phone and Mac.

I'm not sure why you are not seeing some of the SMS texts but first, reboot your Mac and then try to send an SMS to someone from your Mac by typing their name (this will also make sure that the Contacts are working). To make sure you are sending through SMS and not iMessage, your own messages should be in a green bubble. If they are in a blue bubble, it means they are sent through iMessage.

If the above is not working, try turning on Messages in iCloud on your phone (Settings > Your Name > iCloud and turn on Messages) and on your Mac (Messages > Preferences > iMessage and check Enable Messages in iCloud)