Yes, sodium hydroxide (NaOH) is the correct technical name for caustic soda.
Take this one seriously: do not mess with this stuff without wearing safety glasses.
You can tell whether you are dealing with pure NaOH if you touch it with your bare fingers: it feels slippery, because it is dissolving your skin so fast that it forms a slippery layer between the two surfaces.
I regard pure caustic soda as too dangerous a substance to keep in the house, despite warning labels etc. Furthermore it is likely to damage nearby materials. Yes, rather strong caustic is sold as a drain cleaner unfortunately. In the old days you used to be able to buy arsenic, cyanide, and strychnine too. Better sense prevailed with those other substances, but not yet with NaOH. Hopefully, the system will improve eventually.