Web design, hosting and Google search list

I would like to optimize the following website because I think is not really attractive to customer. Since this website has been developed i did not get many customer.
1) Because the name was bad chosen and make it difficult to search in google.
so the address link should be related with the activity of my company.
2) How to make this web to be at the top in google search? What fee should i need to pay to google to have this option.
3) Be able to access to the page and update or modify simple things.

Can you please advice what would the best way to get benefit of this site?
I.e change the name of the web address to be easy to search rather than my name.

Answer to questions that might help on this job description suggested by Prasenjit.
1) What is your website URL?
http://www.osorio-cleaning.com/

2) Are you targeting people locally, nationally or internationally?
I am targeting people National. (UK, LONDON)

3) What keywords would you like to be ranking for?
clearance & waste removal

4) What is your monthly budget?
Difficult to answer , as i am knocking door for getting job at this time. and waitng for customer to get in touch


Thanks,
Regards

Fernando