The tables below show the information I was trying to get for the "math italic" letters in the Latin Modern Math font. The first column shows the slot occupied by a glyph, and the second column shows the glyph's name. As explained in Ulrike's answer, you get the names of the corresponding "script" size letters by appending ".st" to these names. So, for example, a script size "n" has the name "u1D45B.st". Similarly, script-script size glyph names are formed by appending ".sts".
Except for the strange case of "h", the name actually tells you the Unicode code point of the character. So, for example "n" has code point 1D45B. This allows you to find the character easily in the Windows Character Map app, or to include it in a MS Word document using the Alt+X trick. The script-size characters are unencoded (they don't have Unicode code points).
Given the name of a glyph, you can easily find it in FontForge.
The names or "slot" numbers can be used to enter the characters into TeX documents. For example, you can insert a script-size $n$ by typing
In fact, the script-size "$n$" is in slot 1417 in Latin Modern Math, so you could also insert it more directly using
Obviously this is a bizarre and roundabout way to get an "n" into a TeX document, but I have found that knowledge of slots and names is occasionally useful in some odd-ball scenarios.