I think user1133275 has the answer to your question (i.-e. cleaning the DHCP cache), but there are a couple of other things to watch out when "cloning" Linux systems.
First of all, you might want to tune the hostname as well, or you will have the same hostname for all. It is often not a problem, but it is an easy way to find out on which host you are rather than looking at the IP address. You need to change the hostname (or adjust it) in the following files:
It would then be best to restart the network but depending on the Raspbian release you are using (Wheezy or Jessie) it might be different, so just reboot :-)
Regenerate SSH host keys
Second, if you have install the SSH server, all your Raspberry Pi will have the same host SSH keys, so you cannot reliably authenticate the Raspberry Pi you are connected to.
On Raspbian it is easy matter: delete the host keys and regenerate them.
sudo rm /etc/ssh/ssh_host_*
sudo dpkg-reconfigure openssh-server
Note: if the last command fails, you can always manually generate them (if you are still in Wheezy, then skip the last one):
ssh-keygen -t rsa -b 4096 -N "" -f /etc/ssh/ssh_host_rsa_key
ssh-keygen -t ecdsa -b 521 -N "" -f /etc/ssh/ssh_host_ecdsa_key
ssh-keygen -t ed25519 -N "" -f /etc/ssh/ssh_host_ed25519_key
Restore interface name
Third, you might find that the network interface name (e.g. eth0) is different on each Raspberry Pi. It is because each of them have a different MAC address (unique for each Ethernet board) and those MAC address mapping to interface name are stored in the file
/etc/udev/rules.d/70-persistent-net.rules. So on all the "cloned" Raspberry Pi I would edit the file and remove the entry in it. This is a bit more than cosmetic change, if you had some specific configuration or script relying on the interface name, then there will be broken.
Other optional tweaks
Finally, there are other tweaks to perform but it depends of what you are using/installed on this image. For example, you might want to update Samba configuration (the hostname and description), any certificates you created for TLS connections (such as an HTTPS server or for mail server). You might want to change passwords of users (including root if it is activated).