Why would you put lots of zeros in front.  That's just dumb.

When you buy a piece of candy, are you told that the price is 0.00000025 hundred grand?

Of course not.  You move the decimal over and give it a new name: 25 cents.

Bitcoin will be the same.

nanobitcoin will be fine for a few centuries at least.  Most likely a nickname will develop naturally.  Perhaps nanos, or nans, or nanobits.

Metric prefixes can continue to be used if necessary beyond that, but there isn't any reason to believe that people won't come up with their own words.

Perhaps rather than 0.00000000000000035 BTC, people will simply say it is 350 sligshmacks (or whatever other name develops naturally).