No need to modify the dynamo at all Zappa to use it at 12volt unless you want to. But you will need to swap the cut-out/regulator for a 12v unit - there are several options - and of course you'll need a 12v battery and bulbs.
If you wanted to, you could replace the armature and field coil with finer-wound so-called 12v parts - the advantage being that these parts allow the dynamo to start charging the battery at lower RPM. If you do that, you get the same 60W limit of the old 6v system; whereas if you keep the older windings, they can safely deliver about 20% more.
A good combination is to use the dynamo you've got, if it works OK, with a solid state regulator like the DVR2 unit often mentioned here, which is a straight swap for the old cut-out/regulator box, costs about £45 and is available in Positive or Negative earth (and also in 6v form if you decided to stay at 6).
Some electronic regulators may require the internal wiring of the field coil and brushes to be swapped round in the dynamo; DVRs and a number of others don't.
If your dynamo doesn't work properly, then folk like Dave Lindsley can certainly fix it very well, but it's not cheap (£200 to £300?), especially with postage included, and could take a good few weeks. But all the parts (original style or fine-wound coils, plus all the consumable bits like brushes) are available off the shelf, and the dynamos are easy to take to bits.
The Alton alternator is a different sort of 12v option, well-proven and high-output, but again quite an expense at about £320 plus another £26 for the rectifier/regulator to go with it, plus VAT at 20% if applicable. Ie over £450.