Not quite, the phone has an IMEI (as others have pointed out). Some networks have now got IMEI blocking for stolen phones, so even if you put a new SIM in it, it won't work.

Problem is, lots of the phones have reprogrammable IMEIs (if you have the right tools - ie a PC, some software & the right cables). Just recently a law was proposed (passed?) that made (a) changing IMEIs or (b) selling equipment to change IMEIs was illegal.

There's no real legitimate reason to change a phone's IMEI unless it's stolen; removing the network lock is also a bit dodgy as it undermines the pricing model...

Hugo