Thanks for adding this link, fixbutte! It does indeed show clearly that the spelling OkeH, as you said, was the intended one, regardless of the presence or absence of the round "Motor / Record of Quality" logo. The article on page 95 also mentions that the name OkeH is "derived from the original Indian spelling of the term colloquially known as O.K., meaning 'all right'."
Thanks cyeaman for the images of your record with mixed-up labels, and thanks xiphophilos for clarifying the "O.K.E. Heinemann" myth. Although I circulated the story myself, I have been doubting its validity for the last few years, as I have never found an evidence for it.
Still it seems obvious that the first spelling of the label name was not just an accidental layout fancy but meant to highlight the initials of the owner and president of the Otto Heineman Phonograph Supply Co. Anyway, his full name and the OkeH spelling (still without the logo) were prominently placed in the announcement of the first OkeH record in the Talking Machine World issue of May 15, 1918 (full-page advert after page 46 and article on page 95).
I see that fixbutte in a comment below alludes to the old story that the name OkeH had something to do with founder Otto Heineman's initials.
The story that his name was O.K.E. Heinemann, though, is a myth because Heinemann's full name at birth was Jehuda Otto Heinemann. I found his full name on his 1904 Frankfurt am Main marriage certificate. In the US, he seems to have dropped the Jehuda and not to have added any other middle name(s). On his 1915 Declaration of Intention (to become a US citizen), he already goes by Otto Heinemann.
In 1919, "Okeh" was simply a word that lay in the air. People then believed it was originally a Choctaw word that meant "alright". President Woodrow Wilson would sign papers with "okeh." It's probably, in fact, a made-up word (source). In any case, Heineman liked the alleged meaning and its Native American connotations and chose it as the name for his new label (thus the Indian head). It could be that he spelled the label name OkeH to highlight the initials of his first and last name, but who knows. Maybe he just felt that the logo looked better that way, more balanced around the circular "The Record of Quality" logo. As soon as that circle was dropped, in late January 1920 already, the label name was spelled Okeh.
OKeh, founded by Otto K. E. Heinemann (1877–1965), had begun with vertical cut recordings in 1918 starting with cat# 1001 in the 1000s series, but in the autumn of 1919 the company switched to the more common lateral cut method of sound recording. This was the first-ever record in their new 4000s "Lateral" series. The record, with the then typical Indian Head on a blue label, was soon reissued with the better known red-colored label, still with an Indian Head in the "O" of OKeh (or rather "OkeH" then).