Hi ninjacarrot,
Thank you for using the Apple Support Communities.
We understand that you have deleted contacts however, the deleted contacts are still showing up in the Telegram and Snapchat apps and also the old names haven't changed & we are happy to help! To resolve this issue follow the steps in the Apple Support article If your iCloud Contacts, Calendars, or Reminders won’t sync.
If you followed the steps in the support article and you still have issues with deleted contacts showing up in Telegram and Snapchat apps, then we recommend you contact the third-party app developer for those apps, see How to contact an app developer.
Have a good day.