As explained in legend for the the character list, there are some differences between the ISO 8859-1 names and Unicode names for some characters, and even variation between Unicode versions. It is probably best to use Unicode names as defined in the newest version, due to the increasing importance of Unicode.
In addition to official names, there is a large number of unofficial names for characters, and they vary from one context, culture, and group of people to another. For a collection of some of the jargon, see pronunciation guide for unix. For example, for the tilde character ~ it lists the following Unix and C jargon names: twiddle, tilda, tildee, wave, squiggle, swung dash, approx, wiggle, enyay, home, worm, not. For communicative purposes, such jargon names should be avoided at least outside contexts and communities where they are generally known and uniquely understood. And in fact, if you use them in your ordinary environment, are you sure you can smoothly switch to standard names when needed?