Both "jina la kikenya" and "jina la mkenya" are correct. Maybe there are regional (or even Kenyan swahili vs Tanzanian swahili) preferences that cause people to have such strong opinions one way or the other.
I'm not sure why they keep bringing the specific name Juma up in the "jina" lesson. It would be much less confusing to not be first hearing them both a lot at the same time.