The 26 dimensions you mention are specific to so-called bosonic string theory. Adding fermions via supersymmetry cuts this number, also called the critical dimension (because the theory seems to be only well-defined in this number of dimensions!) down to 10. However, this gives you several different theories, which turn out to be connected via dualities.
The covering theory is called M-theory, and in this theory an extra dimension opens up.
I'm not sure what you mean by "naming dimensions". I can name them whatever I want: (t,x,y,z,a,b,c,d,e,f,g,...) :)
What are all the 26 dimensions in the M theory, named?
I thought that M-theory had 11 dimensions? A string theorist named Edward Witten figured that out, last I heard.
In string theory, particles are oscillating vibrating 1d lines, as opposed to 0d point particles. The reason they are preferred, is because they eliminate infinity solns, otherwise known as mathematical anamolies. It's also believed they may help in unifying quantum mechanics with general relativity. The 11 dimensions consist of 10 spatial dimensions, and 1 time dimension, so 7 extra inperceptable spatial dimensions.
If I recall correctly, these 7 extra dimensions are necessary to provide "the required space" for the strings to vibrate, if they are to vibrate in such a way as to support all the known particles of the Standard Model. Ed Witten figured out that the other competing string theories (which assumed less than 11 dimensions) were all the result of looking at the 11 dimensions from limited and differing perspective.
I'm not sure what the dimensions are named either.