Although this surely was not usual we can find some girls and boys, men and women which were known under a different name as the one we can find in the baptismal record. But I would always be very careful and defensive to accept such a identification, it depends on the record situation and on the evidence you have for the interpretation that Eleonore and Klarchen was one and the same person.
That advice could not be stated better or more succinctly. Cornelia was also commonly nicked as Nell or Nellie, but that name would be quite a reach to arrive at Kl�rchen, and not conventionally associated like Klara is. Eleanore as you know is most commonly nicked as Elaine, Ella, Ellie, Ellen, Helen, Lanna, Lena, Nonnie or Nora stateside -- beyond Nell or Nellie. Cornelia shares many of these diminutives also.
Though the evidence you have points to an alignment Don, I'd always be careful in assuming too much without additional supporting data, as some rather flimsy conclusions can be "conveniently had" when one starts presupposing freely without the requisite back-up. I have seen plenty of unsupported claims based on just this sort of thing that later were proven oh so incorrect.
My first guess was that Kl�rchen would be a nickname for Clara/Klara. We know this is the same person as Eleanore because the husband and the children listed are all correct and the age for Eleanore/Kl�rchen is correct. She emigrated to the U.S. with her husband and children in 1857 with the name Eleanore. I guess it is one of those mysteries.
I was going to tell you about another mysterious name in my family. My great grandfather was born and baptized in Lendorf, Hessen in 1850 with the name Johannes Kn�pfel. That is the only name which can be found in the records of the Evg. Luth. church there. He was called John by his brother's and sister's but he used the name John G. and Gustav J. No one has a clue where the name Gustav came from. It surely is a name of its own and not a nickname. I guess he may have just liked that name. There is no one alive today who would know.
The other obvious consideration would be the use of a middle name as a preferred one, that is, in place of the given one. This practice was commonplace years ago, and still lingers on today at times. Someone named Gustav Adolf might be better known as Adolf or Dolf; conversely a person named Adolf Gustav might be known as Gustav or Gustave or Gus. I have seen occasions where both first and middle ones are freely used at the same time (interchangeably), or depending on a certain family member or relative's preference. Perhaps you will find a Gustav who figures somewhere previously in the family lines. Not to digress, but it was also somewhat trendy, particularly in business circles during the latter half of the 19th century here in the States, to use one's initials in place of their given names. Thus A.G. Smith or G.A. Smith, per the examples previously used. [sometimes a great way to find pointers to an ancestor's middle name]