Vati (Vatt)
Being next to Lambi, which could be mistaken for ‘Lamb street’ (it’s not), it might suggest wadding, padding, cotton wool (from French ouate) or, by extension, a short jacket or clothes. But no, false friends: lamp:lambi is a lamp and Vatt:vati is a Watt, so be careful with your abbreviations. 10th of a septenary* selection of sparky streets. See Juhtme.
* Maths joke. Don’t worry, I didn’t even get it myself on proof-reading.
Tornimäe (Tornimägi)
Although it means Tower Hill, there’s neither one nor tother in sight. Apparently named after a certain Adam Tornimäe (or Adam X from Tornimäe in Saaremaa), a worker who rented a property from Jaani Seek, St John’s Almshouse, in the early 17th C, long enough for it to become known as Tornimäe Maja (house). In the 19th C, Tornimäe was also the place to go for autopsies. See Mäe for discussion.
Kuke (Kukk)
Cock, rooster. Formerly spelled Kukke and significantly shorter than its present-day layout, it curved around a smaller and shorter Kana tänav. Why these names? Your guess is as good as mine.
Vile (Vile)
Whistle. One of a small locomotive-themed group next to Tallinn-Väike station. See Auru.