Hi Paulette,
I think using Astoria Business Solutions is a good start in terms of
SEO for your site (if you do want to try to rank for local search). But if you specialize in something in particular it might be a good idea to work that keyword into your business name as well as, or instead of, 'Business Solutions' (because I'm not sure anyone searches for 'business solutions' (though you could always check with the Google keyword tools they offer). 'Astoria businesses' is pretty vague and probably not something a potential client is going to use to find you or your services.
Of course you'll have plenty of opportunity to optimize for more targeted keywords with the content on your site (and blog, if you have one) so you could certainly go with the more generic business name and then work like crazy to rank for your actual services.
I'll look forward to hearing back when you decide what to use!