My website to appear in google when searching the specific company name

I launched my website about 2 months ago now, and was advised it can take up to a couple of months for it to appear properly in Google. 2 months on, and when you search for the company name, Google still doesn't retrieve my company website: www.connecteditrecruitment.com - I do not want/need any advanced SEO for specific key words, etc, all I want is that when someone types in google "connected IT recruitment" , my website is easily visible. Can someone please help, and give me a price to get the job done?

This doesn't seem to be an issue for anyone else who publishes a website - I have several friends who have websites and pretty much as soon as it is launched Google retrieves their site when you search the specific company name. I'm unsure why mine is any different?

Thanks