Snapchat does not offer a built-in feature to change the color of your display name directly within the app. The display name on Snapchat is typically displayed in white or black, depending on the background color.

However, Snapchat provides an alternative method to customize your display name by using Bitmoji, which allows you to create a personalized avatar. Here's how you can change your display name color using Bitmoji:
How To Change Your Name Color On Snapchat?
Install Bitmoji: If you don't already have Bitmoji, download the Bitmoji app from the App Store (iOS) or Google Play Store (Android) and create your Bitmoji avatar. Follow the prompts to customize your Bitmoji to your liking.

Link Bitmoji with Snapchat: Open the Snapchat app and access your profile screen by tapping on your Bitmoji avatar or the ghost icon at the top left of the main screen. Tap on your profile picture and select "Create Bitmoji" or "Change Avatar" to link your Bitmoji account with Snapchat.

Customize Your Bitmoji: Once linked, you can access the Bitmoji customization options within the Snapchat app. Tap on your Bitmoji avatar in the profile screen to open the Bitmoji customization menu. From here, you can change your Bitmoji's appearance, including the outfit and style.

Update Display Name: After customizing your Bitmoji, return to the profile screen in Snapchat. Tap on the gear icon at the top right to access your settings. Scroll down and select "Name" under the 'Who Can...' section.

Add an Emoji: In the Name settings, you can add an emoji before or after your display name to give it a unique look. Find an emoji that represents the color you desire and add it to your display name. Keep in mind that the color of the emoji may affect the overall appearance.

Save Changes: Once you have added the emoji to your display name, tap on the checkmark or save button to confirm the changes. Your display name will now include the selected emoji, potentially adding a splash of color to your profile.

It's important to note that the above method only allows you to add an emoji to your display name and not directly change the color of the text. The available customization options within Snapchat are subject to change, so it's always recommended to check the latest updates and features from Snapchat itself or refer to their official support documentation for the most accurate and up-to-date information.