Alicornutopia

That would be fine by me.

Might as well.

Sha-1: 85b5aa2e1042b3f2a0e303bd3f25d4c34786138e
Allowed strings: Anything with uppercase or lowercase letters (A-Z, a-z)
Projected difficulty: Not that hard

My rule has an opinion on Noldor politics, so
Yes: Feanor
No: Fingolfin

By “with” do you mean “consisting entirely of one or more”? Otherwise I want to try the empty string, F1, and Féanaro.

Feano
Feanol
Fenol
Finol
Fingol
Fingolf
Fingolfi
Fingolfin

feanor
fingolfin

You are right, that was ambiguous.

Allowed strings: Anything consisting of uppercase and/or lowercase letters.

Yes: Feano, Feanol, Fenol, Finol, Fingol, Fingolf, feanor
No: Fingolfi, Fingolfin, fingolfin
(I'll write a infobox generator code tomorrow, so it's ugly for now.)

Feanors
Feanori
Feanar
Feanara
Feanare
Feanari
Feanaro
Feanoru

Fingon
Findekano

Still ambiguous; is the empty string well-formed?

If you have Python 3 and can express the rule in it (where input("Is " + guess + " valid (y/N)? ").lower().startswith("y") is a reasonable option), you can use my infobox generator which I’ll post tonight.

Let's say the empty string is not well formed.

Yes: Feanors, Feanori, Feanoru
No: Feanar, Feanara, Feanare, Feanari, Feanaro, Fingon, Findekano
(I ended up writing my own infobox generator, as I'm using python 2.7)

Random words to get a variety:
Arda
Eru
Ea
Valinor
Mandos

balrog
orc
dwarf
human
ent

All yes.

So far all the Nos are six characters or more and all start with F. Let’s see if that continues. Even if it does it won’t prove anything, because both of those, even combined, are in the Yes list, but if not it might help.

Fin
Fi
Fee
Fo
Fum

supercalifragilisticexpialidocious
kuuskytkolme
sixtythree
Alicornutopia
Submit

Yes: Fin, Fi, Fo, Fum, Submit
No: Fee, supercalifragilisticexpialidocious, kuuskytkolme, sixtythree, Alicornutopia