@rr2022: The search function in the Contacts app should produce results for the name assigned to your contacts. To troubleshoot the issue, try opening the Contacts app > Tap the 3 lines in the top left > Tap the cog in the top right of the pop up window > Sort contacts by > First name > Name format > First, last.
Head back to the Contacts home page, tap the magnifying glass in the top right, and search for the relevant contact. If the issue persists, scroll down and double check that the name of the contact is correct. If it isn't, tap on the contact > Tap the pencil symbol at the bottom of the screen > Tap the drop down arrow to the right of their given name (this should be positioned at the top of the screen) > Make the necessary changes > Save.