The location shown on your CVs comes from your account, not from the CV itself.

1. Open My account.
2. Type your town in the location field.

3. Click the suggestion that appears. This is the step most people miss: until you click a result, the town isn't saved. The map on the right updates to confirm it worked.

4. Then open your CV's administration, change any field — one line of description is enough — and save.

That last step matters: saving the CV is what pushes the new location to the search engine.