Yep, it's "umeme" in Tanzania and "stima" in Kenya. I believe that "umeme" also means lightning, which is a nice connection.
The correct word is umeme, LUKU is what Andreasll has mentioned. Tanzanians have a tendency to incorporate major brand names into the language if the product has become ubiquitous in the country. E.g: Motorbikes and scooters are known as Honda and Vespa respectively instead of pikipiki. If Elon Musk were to flood East Africa with his cars, Swahili speakers would no longer call them "gari" they would call them "tesla".
And this isn't just common to Tanzania or Swahili - see e.g. "bandaid" (USA), "hoover" (UK) etc.
Most Tanzanians I know say luku rather than umeme. I guess it's slang or common usage?
"Luku" is the prepaid electricity you buy from TANSCO, the national utility. It's an acronym for "Lipa Umeme Kadiri Utumiavyo" (I'm not sure about the translation, but I think it's something along the lines of "Pay for the electricity that you use". You buy it a shop or on your phone, and it gives you a code to punch in on your electricity meter at home, to "recharge" your available kilowatt hours.
Maybe they have started using this name for electricity in general in some areas.
Thanks. I wondered about its origin. In Dar es Salaam people talk about buying luku in everyday conversation. I've not heard anyone say they are buying umeme.