You don't say what app or platform you are using, but if you are using FL Studio you can define your own .enc file and FLS can use it. Check the manual (page 154) or the FontLab Forum for more information about your particular platform.

I'm using FontLab on PC. And I already have my .enc file ready to use.
The thing is that when I use my encoding in FontLab those glyphs have the wrong Unicode.

Someone here may chime in with an answer, but I don't have it. If I encountered that problem I would ask about it in the FontLab Forums.

Name-to-Unicode mappings are stored in .nam files in the \FontLab\Shared\Mapping folder, independent of the .enc files in the \Encoding folder. So you set up the name-to-Unicode mappings in a .nam file, and then use those names in a .enc file. In FontLab, you then need to use the 'Generate Unicode' dialogue in the Glyph/Glyph Names menu to select a default .nam to use. [Note that every once in a while, FontLab will revert to its Standard .nam and you will need to reset the default.]

PS. I recommend creating your own .nam files, even if based on those provided by FontLab, rather than editing the Standard .nam.

I can't seem to find standard.nam anywhere, though I do have a folder \Fontlab\Shared\Mapping that contains readme_nam.txt.

Where should I look for it -- or is my [Windows] FL Studio 5.0.4 installation deficient?

Somewhat confusingly, FontLab can store .enc, .nam, etc. and also macros in more than one location. The default location on Windows is not the folders in FontLab's app folder, but the ones at [User]\My Documents\FontLab. Check there.

Sorry my earlier post didn't come through as I intended, but I was looking in [Users]\My Documents\Fontlab. :-(

Oh, try the FontLab folders in Application Files.

Thanks everyone this has been very helpful!