I publish under a one-word name, which Google Scholar does not index. What can I do?
Google scholar is imperfect. It's based on an automatic parser, rather than human curation. I've seen it make all kinds of mistakes.

What can you do? You already have set up a profile that has the correct information. You can try contacting Google, but don't expect much from them. I doubt they have the resources to deal with everyone who contacts them with an issue. However, they are always improving their algorithm and this may get resolved.

The only other thing I think you can do is alter how your name appears on papers to conform to western expectations, as suggested in this question: I have only one name shown in my ID card. How do I write my name (surname) in research paper or article?

Overall, I wouldn't worry too much about it. It is easy enough to find your publications online and any human reader will understand that you are mononymous.