I'm new to wifi. Do I need a wifi router or can I use my mac mini to provide the wifi? thanks

While a Mac mini can provide a Wi-Fi network. its range and power will be lower than a dedicated Wi-Fi router / access point

To share your internet connection to other devices over wi-Fi your Mac mini will need to be connected to your Modem via an ethernet cable.

See here: link-> Share the internet connection on Mac with other network users - Apple Support

That's an entirely different proposition all together.

To connect it to your Phone, you need to turn on Personal Hotspot in the iPhone in Settings->Personal HotSpot. See here: link-> How to set up a Personal Hotspot on your iPhone or iPad - Apple Support

Once that is done, from your Mac, you can look for your iPhone's name in the list of Wi-Fi networks in the menu bar. It may appear in the "Personal Hotspot" section. When you find it, you can click on it, and then provide the password you set in the previous step.

Your question is a bit confusing now. Are you wanting to share a Wi-Fi connection form the Mac mini to other devices, or are you wanting to connect your Mac mini to a wi-fi network? Those are very different things.

The Mac mini can create its own Wifi network to share with other devices, as such you would not be looking for a specific Wi-if network from your Mac. As mentioned the Mac mini would be connected through an ethernet cable to your modem.

When setting up the Wi-Fi network for other devices from your Mac, you can give it whatever name you want. That's part of the setup.

If what you want, is to connect your Mac to your internet provider's modem over Wi-Fi, then yes, you should be looking for whatever Wi-fi network it creates. The name and password can usually be found on the bottom or side of the modem.

If your modem is not capable of creating a Wi-fi network, then your Mac cannot connect to it over Wi-Fi.