You need to get the FIT transferred into your name with SSE. This should have been clarified during conveyancing.
We don't have storage batteries, so a bit different. However, any electricity you use whilst it is generating (sunny daylight) will not register as usage on your BG meter. Then whatever excess is stored and used from the battery also won't register on the BG meter.
So, you should find that your usage and bills from BG are very low, especially in the summer.
Depending on when the panels were installed and registered for FIT, you will be paid by SSE separately for what you generate and (in most cases) for half of this that is deemed to have been sent back to the grid. A battery might prevent you being eligible for the latter, but the rate for this is very low anyway.
Most importantly, have you taken a reading from your generation meter? If not, do this ASAP, as you will only be paid from your earliest reading.
It took us 9 months to change the FIT ownership, but as I had a photo of the generation meter reading from our first day, we got the back payment. Ours is an early install (2011), so our FIT is at a generous rate. We received over £2k last year.