I want to pursue topics from different fields (pure math,CS) as a researcher. Which one to choose for my PhD?
Generally speaking PhD studies are all about specialization. One dives very deeply into a narrow field. This is especially true of math and can also be true of CS, depending on subfield. 

There can be exceptions and some synthetic work is possible, but it depends a great deal on your advisor and what he or she is comfortable with. If you can find an advisor at the intersection you should be able to pursue a joint approach. 

After the PhD you are much freer to pursue your own goals not constricted by the concerns of your advisor. I would suggest, pretty strongly, that you explore your wishes with a doctoral supervisor and take their advice. If the advice is to pursue the one field for now, it isn't a decision you need to live with for all time. But the advice will likely be good advice. 

Doing a second doctorate will probably be superfluous. You will have deep research experience from the first. If it is in math, much of what you learned will have some application to thinking about some of what is important in CS. 

Doing two doctorates simultaneously seems masochistic to me, especially as you will have two advisors each with different, possibly conflicting, expectations and each putting constraints on your time. 

Think specialize now. Think widening interests for the future. It will better match the expectations of those around you and make life easier. 

But you will also need ways to not get bored, given your description of the problem. It might even be that while focusing deeply on one of the fields you can 'play about' in the other for a short periods just as a stress reducer as needed.