Hi Norma,
Deciding on a name takes a long time and so it should, as you will be living with it for a long time.
You are also correct with regard to your domain name. My official business name is CĂșile Virtual Administration Services which is very long but I use the initials as my domain name CVAS. I purposely went for a name that could be abbreviated easily as it is easier for people to remember if they want to visit my site a second or more times (that is before the work with me then it will be in their contacts and they will never have to remember it again!

)
So take some time and try out lots of names and play with them, write them down, say them out loud, pretend you are answering the phone and using it like that. But most of all make sure you like it and it suites your business.