Hi Charlie,
Congratulations on getting your Tapu.
Yes, you need to change the water and electricity into your name.
If you used a lawyer or estate agent they should help you with this. If not, for electricity, you need to go to Aydem on the road out of Fethiye towards Karaculha and it is on the left coming from that direction. They need a Tapu copy and will ask for either 1 or 2 copies of your passport. If your property has been a resale, the person that you bought from needs to go with you with their abone number (account number).
For water, we found that we needed to go to 2 Feski offices. Again you need to go with the previous owner if applicable with account number, and you need Tapu and passport photocopies. Go to the Belediye office in the centre of Fethiye, this is above Migros. Go to the desk on the left which deals with water bills and you do some paperwork there . Next you go to the office along the canal near the otogar, - going towards Olu deniz from Fethiye, go past Carrefour Express and cross the canal and turn immediately right and go along the canal. The office is about 100m along on your left. You should complete there.
Hope that helps, Cathy