Yes you can! You can set up a default Caller ID for each user in your dashboard at Dashboard > My VoIP > Users .
However, you can also elect to present a different Caller ID for each call you make by creating a short code. This is a code that you type into your phone before dialing the number you wish to reach. So for example, if you had a short code of * 22 to present the number 01296 252 001 you would dial *22 and then your number.
To configure these short codes, simply visit Dashboard > My VoIP > Config > Short Codes and set up as many as you would like. Note that some hardware "reserves" certain short codes for use on their specific hardware, so if your chosen short code doesn't work first time, just pick another short code number or login to the management interface of your phone and in most cases you can disable what is often referred to as "Local Call Features".