The blinking circle that appears above a person's name in iMessage or normal SMS is most likely a visual indication of ongoing communication activity. This is common in messaging apps and simply means that the message is being sent or received. It is important to note that this behavior is not a security issue as security issues typically manifest differently and blinking circles are not an indicator of any security concerns.
Potential reasons for this behavior could include:
1. Network Activity: The blinking might occur during periods of network activity as the message is being sent or received.
2. Data Synchronization: If your contacts are linked to social media accounts or other online services, there might be synchronization activities causing the blinking.
3. Software Glitch: Occasionally, software glitches can cause visual anomalies. It might be worth restarting your device to see if the issue persists.
If you're still concerned or if the issue persists and seems abnormal, you may want to consider reaching out to Apple Support or checking for any relevant updates for your device's software. They can provide more specific guidance based on the details of your device and the latest software version.