No, if two objects move away from each other at the same speed, there would not be any significant time dilation between them. Time dilation occurs due to relative motion or differences in gravitational fields.
Time dilation is a consequence of the theory of relativity, which describes how time can appear to pass differently for observers in relative motion or experiencing different gravitational fields. Specifically, there are two types of time dilation: time dilation due to relative velocity (called "velocity time dilation") and time dilation due to differences in gravitational potential (called "gravitational time dilation").
In the case where two objects are moving away from each other at the same speed, they would be in relative motion but with no significant difference in velocity. As a result, the time dilation between them would be negligible. The observed time for each object would be relatively the same, and their respective clocks would tick at a similar rate.
It's important to note that even though the objects are moving away from each other, their relative speed is what matters for time dilation, not the absolute speed with respect to an external frame of reference.