It can sometimes become necessary to see the Timestamp or the exact time, when a particular message was sent from your iPhone or received on your device.
The reason for this could be to check your own performance or promptness while replaying to messages or to prove that the person at the other end was late in responding to your important or urgent messages.
Luckily, iPhone does record the Date and Time of all incoming and outgoing Messages and it is possible to check the exact Time & Date of all the messages received and sent from your device.
See Timestamp of Messages on iPhone
While iPhone does record the Time/Date of each and every message sent/received on your device, it displays the Timestamp only for the first message sent or received in a message thread on a given day.
However, the recorded time of each and every message on your iPhone is still attached to the messages and it can be easily viewed by simply dragging the message to the right.
View Hidden Timestamp of Text Messages on iPhone
At any time, you can view the hidden Timestamp of practically any message sent or received on your iPhone by following the steps below.
1. Open the Messages App on your iPhone.
2. Open the Message of the person that you are interested in.
3. On the next screen, locate the particular Chat that you are interested in and drag your finger from right to left in the message area and hold your finger on the screen.

You will be able to see the Timestamp of all the individual messages in that particular conversation, as long as your finger is pressing and holding on the screen.
Lifting the finger from screen will cause the Timestamp of the all the individual messages to become hidden again.