to store your contact on SIM card is probably not what you want except if you don’t want to store more than name and phone number. I don’t even know if recent Android supports this storage. But you can try a Contact editor (I use contact editor pro from dmfs GmbH on Play Store) which allows to store your contacts on your phone memory. Useful, if you cannot sync to your cloud e.g. with DAVdroid on F-Droid.
To tell the truth, that’s exactly what I do want, as I don’t need much info about my contacts.
The fact is, before installing the Open Gapps pico package (which made a link between google accounts and my phone) I had the possibility to simply add a contact to my phone, to my SIM card, without even any other app needed… That’s kind of what I’m looking for, of what I would like to be able to do again. But if it’s not possible, I’ll try Contact Editor Pro as you said