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indeed this name is closely related to William, Whilhelm, Wilhelmina, Wilhelmine, Guilhem (in France) or even Guillemette (still in france).
wilhelmina is the name of several queen of netherlands and there are streets, parks, and avenues called that way.
I know that you can break Guilhemine in two parts made of the two english words will and helm (i know the traduction in french but it won't help since you speak english.
I never met myself anyother guilhemine (with a lh and not ll!) but I heard of some of them.