Hello brendafromport Washington,
It sounds as though names are autocorrecting to each letter being capitalized versus just the first letter when typing the name Cory. Apple Support Communities is a great place for help, and we’re glad you had the opportunity to verify the name in Contacts, and review the related article which we’ve linked below also.
How to use Auto-Correction and predictive text on your iPhone, iPad, or iPod touch
In addition to the steps you’ve already tried, have you checked to see if there may be a text replacement as outlined in the related article? If not, you can verify if any text replacements exist by going in to Settings > General > Keyboard > Text Replacement.
If you continue to have issues after removing that text replacement or a text replacement doesn’t exist for Cory, the next step would be to reset the keyboard dictionary. This can be done by going in to Settings > General > Transfer or Reset iPhone, tap Reset, then tap Reset Keyboard Dictionary. By resetting the keyboard dictionary this will remove any words that you’ve added by rejecting words your iPhone has suggested as you type. This information can also be found in the following article.
Return iPhone settings to their defaults
Let us know how that goes!