Moved 6 miles away. Must I tell the HO?

Many apologies if this is a dumb question. However considering immigration is getting tighter and more complicated, I'd like to just be safe.

My family moved from one rental to another, just 6 miles away last October. I have waited until now to send off the D1 form to the DVLA and the other thinga ma jig to have the address on my driving license changed, as well as changing to my married name.

Is changing the address and my name through the DVLA sufficient? Or do I need to send a letter off to the Home Office to let them know? I'm just thinking if I plan to take the "life in the UK" test and apply to be a dual national, will filling out forms with a different address bite me on the bum?

As far as I can gather, (have never read anything saying otherwise) the HO aren't like the USCIS in that they don't require you to inform them when you move house.

We've moved once already since Hubs entered on his spousal visa and we will be moving again at the end of this month.

nope, the HO doesn't need to know if you've moved.

Thanks to the both of you. Just don't want to get deported. 

Laura