My biz name came naturally because I have been called "The Office Goddess" for nearly a decade. A biz name should reflect your personality and feel 'right' to you; don't rush it.
THIS thread may help you get started. The tagline will come after your business name is determined.
You may consider parlaying your name into a tagline - something like "Esmerelda Virtual Assistance - bringing you a jewel of excellence". Keep in mind I am TERRIBLE at both biz names and taglines so please, DON'T go with this suggestion; it's just to get your mind thinking.
As far as doing a website, many of us set up our own from the get-go.
THIS sub-forum on VAF will help you get started there, as well.