Welcome to the forum!
If you were to try renaming fonts, they would need to be renamed in Windows (or whatever operating system you're using). Inkscape only uses fonts which are installed on the computer. Although I don't know for sure, I've never heard of doing that, and guess that it's not possible. Well, not easily possible anyway.
I don't know much about how fonts are made, but at some point during the process, the creator gives it a name. So I guess you'd have to go back to whatever point that is -- so that when you install the font in Windows, it has the name you want. I guess there must be certain programs which convert the drawings (of characters) into a font, and I guess that's the point where you would be able to rename them. Note that the font's license might make that illegal, by the way.
However, when you use a new font, the next time you open the menu, that font will be at the top of the list. If you're using only a few fonts, and every time you use Inkscape, then those fonts will stay at the top of the list. But if you use Inkscape one day, and you don't use the Text tool, the fonts will disappear from the top of the list, and only be down in their alphabetical order.
Inkscape allows you to choose a default font. And that font is always at the top, no matter what. Although in my experience, the default font changes on its own, from time to time. I guess I should report that as a bug, except I don't really have any clues how it happens. I just know that suddenly one day my default font has changed.
And finally, there's a little trick I use, since my font menu is SO long, so that I don't have to scroll it so often. Instead of typing new text, and going to the menu to choose the font, I'll just copy existing text which uses that font, and either highlight or backspace, and type the new text. Then it comes out in my desired font from the start.
I have to say, that might be a nice feature. I don't know how hard or easy it would be to do for developers, but if you wanted to request a new feature, such as reorganizable fonts, you can do that here:
https://launchpad.net/inkscape
