If you are seeking to replace the motor on your Dyson DC03, it is called a “YDK” motor and will have the code “YV920” on the side. There is only one type fitted to all Dyson DC03 models.
The DC03 motors are quite sturdy units. They were used in the Dyson DC03’s back when Dysons were still made in England in the late 1990’s. However, fifteen years or so later, the odd one is starting to fail now.
They are still available new, but are quite expensive compared to the value of your Dyson DC03 machine now. Many of the ones available are cheap Chinese knock-offs that will last nothing like the period of time your old one did.
As the originals were so well built, consider buying a quality used one. Not only is it green as you are recycling, but life expectancy should be just fine as long as the one you buy is properly tested and not sparking near the armature when in use.
The picture below shows you the YDK YV-920 motor, so you know what you are looking at.