Can I place one person on the do not disturb?

You can block them. Go to their information in Contacts. Tap "Block this Caller". You can put them in DND in Messages (only affects Message). In the conversation with them, tap on Details in the upper right corner. Turn on Do Not Disturb. You can buy/create a silent ringtone/text tone and assign it to them in their entry in Contacts...

If you're talking about text messages, then yes, you can.

If you're talking about calls too, then no, unfortunately there is not a way to do so. You can however block them in Settings by going to the Settings app, scrolling down to Phone, tapping "Phone" and then tapping Blocked and then tapping "Add New..."

I hope this answers your question.

Best regards,

Austin