Technically, yes, this will be a problem. But there is a way to resolve it.
Because the surnames on both documents are not the same, the immigration/customs officer may not think that this is the same person or may think that the visa is fake. This has happened to my family member before because of the maiden name vs. non-maiden name. She had 2 official documents within the passport but with 2 different surnames (similar to your situation).
The way she resolved it was by getting a notarized letter from the embassy explicitly stating that the person with 2 different names are in fact the same person. She generally only presented the letter whenever the immigration/customs officer asked. So sometimes, the officer didn't notice. But if they did, she always had the document as a backup.