Dear Paul K,
Thank you for reaching out to the community again today.
Since I don't know which country your brother is in and how the responsible authorities deal with visa applications there, it is hard to give you a proper answer to your question.
Based on similar questions on our platform, I assume that the authorities/ the embassy would ask your brother about the different date of birth/ name when they check the system for information about him. If he is invited for an interview, he can explain in person why there was a mistake when he applied for asylum. However, it may happen that his visa application is rejected (also considering his rejected asylum). In that case, there is still an option to apply again or even appeal the decision.
Here is some general information about Schengen visa for family members, relatives and friends: https://www.schengenvisainfo.com/visiting-friends-relatives/
Also, a list of the "12 Common Reasons Why Schengen Visa Applications Get Rejected": https://www.schengenvisainfo.com/news/common-reasons-visa-applications-get-rejected/
I hope this information helps a bit. Feel free to reach out to us again if you have any more questions!