Thank you for the above comments. Please note that changing the HD to an SSD, was a 5 minute job, literally. Ok i did some research online (like youtube) before i carried out the work, but it is dead easy and can be done by anyone.
The multiple names problem seems to have gone away on my Macbook, for now.
I also had this problem when i just upgraded from Mavericks via the App Store. (on the old HD). In fact, it wasn't hanging the name, just was adding (1) (2) (3) etc next to the computer name at irregular intervals and i not figure out why. I had tried correcting this in System Preferences -> Sharing -> Computer Name, but it hadn't worked.
However, i agree that there seem to be some connectivity issues with Yosemite. One example that applied to me, there was difficulty connecting to my time capsule, and the way i solved this was by resetting the TC and letting Yosemite rediscover it as a new TC. I consider this has to do with communication protocols that could be different on Yosemite. Before i applied this solution, i had to restart my Macbook regularly, and this would enable the TC to be connected. One more problem i had, was with my magic mouse. Before i performed the clean install, i would lose connectivity with the BT mouse, after a computer sleep mode. This was indeed very frustrating, but again it is gone now.
Now thankfully, everything seems to be ok. But i have to be honest, i will not automatically upgrade to the next OS X release in the future. Not until i see what problems other people face. I wasted considerable time in fixing the latest problems, and although it is like i have a Ferrari now (brand new super fast laptop) i would have been happier if Apple advised their users to perform a clean install rather than an upgrade from Mavericks.
For the record, my MacBook is mid 2012, i7, 15-inch MacBook Pro, model 9,1 (non-Retina).
I will also add that Yosemite is an excellent OS, it is like a breath of fresh air. And i also know that Apple will fix whatever issues are still there, in a very short space of time. But i have two more devices an iMac and a MacMini. Do i want to go through the same as i did for my MacBook (i.e. clean install)? Not for a while!!
Paris