Applying to jobs in multiple disciplines. How much does name of degree matter?
Before I say anything else, I want to say that the answer to this can't be easily generalised and very much has to do with the particulars of your discipline(s). Mine isn't going to be like yours and without telling what A and B are, any folks here with direct experience will not be able to offer it. 

That said, I have a BA, and MPhil and a PhD in "apples" and for the past 7 years have been permanently employed by an "oranges" department". If I told you what the two subjects were you would look at me blankly as you tried to figure out how there could be any connection between the two. To say that there isn't crossover of people between the two disciplines is an understatement. That said, about 4 years ago I was offered (and turned down) a promoted position in an "apples" department ("oranges" matched the offer), I've had some "apples" departments attempt to poach me, and I'm considered an applesologist among other applesologists still, while mostly passing for an orangologist in those circles. I am now moving to another University's "oranges" department. I'm keen to stay in "oranges" as there is a lot more funding in that field and PhD students that I graduate have a much better chance of finding work than if they were in "apples". 

This is the long way to say that if your A and B are close enough that there is any crossover whatsoever amongst the faculties and researchers you are looking at, you are likely fine where you are. I've always found that what research I do and how well I do it is far more important than what discipline is printed on my degree (because seriously, the two disciplines I am set between are like apples and oranges). If your current location gives you excellent support and the opportunities you need to do excellent research, and as long as you keep your network going across both A and B, you should be fine. Generally speaking...