My son knew my cell number from about the time he was 3, HOWEVER, we kept our addresses (we've moved fairly frequently) from him on purpose.
My son is *super* social, and it's taken years to not have him invite *everyone* over to our house at all time. I'm talking *everyone*. Kids, adults, grocery store clerks, gas station attendants, coaches, my students (college), classmates (ditto), coworkers, husband's coworkers, the list goes on. Whenever he has figured out our address it's ended up being a race to cut him off before he can announce it to the world at large.
Not until last year (at age 7), did we finally get the concept of "there's a time and place" ground in. Stranger-danger didn't really apply because these were all people we "knew", and I was always present. It wasn't so much the people that we knew that were a problem, it was the fact that this was out in public and OTHER people could overhear our address.
Even though my son has known my cell for a long time, until this year (8yo), whenever we were somewhere crowded (county fair, seattle public market, fisherman's warf, disneyland, waterpark, fireworks show, etc.) I'd write my cell number in sharpie on his arm. Anywhere he could *possibly* get lost (never did), under the theory that some people might not either believe a toddler/young child knew the real number, or wouldn't think to ask, OR that he'd get so flustered he'd *forget*. (And also so that any possible kidnappers would have a number to phone for ransom ;) At sporting events I STILL write our section, aisle, and seat number on his arm in sharpie (that's actually been useful more than once).
As far as names... my son is funny about this. He's always been very PRECISE. It's never 1130 at our house (well, twice a day it's 1130). Instead it's 1128, 1134, etc. So it's not that surprising he *despises* the title mum & dad out in public. He will *only* call me Mum in PRIVATE. If we're anywhere where anyone else can *also* be "mum", including at MY mum's house, he calls me R.. When asked what his mum's name is, he gives out my FULL 4 name + maiden name and a brief description, just in case there MIGHT be another R. x, y, z, nee q. Unsurprisingly, he's also a real science guy.
Again, he trumps the need for privacy with the "correct" classification of who his mum is.
So in my experience:
Phone number: As young as possible.
Address: As late as possible