My borther's name is Daniel and my mum hated Danny for a nick name, so while he was young anyone that called him Danny she'd correct them and say he's name's Daniel, we prefer no shortenings. Then when he was old enough she tought him to do the same, he'd say my name is Daniel, not Danny, please call me by my name. It wasn't until he was about 16 that he started getting Dan and evenyone was happy with that.

Why do I say all of this??? Cuz you can definately do the same, if they say Izzy, just correct them and say, We'd prefer you call her Bella or by her full name thank you. Easy done

With DD we had to have a talk to SIL as she was calling her Tears, which I HATED!!! She's not crying, thats not her name and thats not even a shortening, so just said we don't appreciate it and we feel she is too young for a nick name just yet, so Tiera it is. I must say it took a bit of pounding into her head as she is a little stubbern sometimes, but we got there.

Don't change the name you love just because of a nick name, it is always something you can get around. Good luck with it all!