Rename database, html code and web optimisation

Hello, I recently let someone do a check on my Blog and they came up with a whole bunch of issues which I like to be solved. One thing I want to make sure: I do NOT want to LOSE any backlinks. When I got a new layout, my web hosting made a copy of my website so I could work on the copied version and work on my new layout there. Then.. when my layout was done, they made the copy of my website, the live one. The copy of my website was named "Goudjaar", but with changing the live and copy one, they switched goudjaar to my normal website "ladygoldapple". However, my database is still named "Goudjaar", which I find weird and this shouldn't be like that. I probably don't sound very logical, but if you want more explanation: just ask me. Hope someone can help me out with this. Please note I'm just a poor student who likes to blog :)