Yes, you can request authorship under a different spelling of your name. However, it's important to ensure that the spelling you use is consistently associated with your research output, especially if you intend to maintain a coherent author profile. When submitting your work or requesting authorship, clarify that the alternate spelling is an accepted variation of your name, and it may be helpful to include a note explaining this in your submission or correspondence with the publisher.
Claiming your authorship will be easier if you indicate the other spelling in your profile. See "How do I add an alternative author name?" in https://help.researchgate.net/hc/en-us/articles/14292898263057-Updating-your-account-name for instructions. See also "I’m having trouble confirming authorship of my publications" in https://help.researchgate.net/hc/en-us/articles/14292798510993-Authorship for more useful instructions.