There is no absolute right to be able to use your own name despite the existence of a trademark of such name so you will want to search. You may use the name so long as it is not trademarked in the category that you are intending to use it in. For instance, if you are a talent agency and there is another talent agency with a registered federal trademark for "Young Agency" then you may be infringing on their trademark. Even if there is no federally registered mark, someone may have common law trademark rights to the name. Common law trademark is limited in geographical scope (in addition to the category of goods/services) so if there is no one else using the mark in your geographical area in the same category of goods/services and no federally or state registered mark in the category, then you will be fine to use it.
A quick search of the USPTO database did not result in any live federally registered marks for "Young Agency," "Young Marketing" or "Young Group." A quick search of the Arizona database pulled up a few Young Agency's so you should check to see if they are in the same category of services as you (I assume that you are a marketing firm):
F10169165CORPORATION YOUNG INSURANCE AGENCY, INC.
10581840CORPORATION ***** ***** AGENCY, INC.
F12312361CORPORATION RODNEY D. YOUNG INSURANCE AGENCY, INC.
623885TRADENAME THE YOUNG AGENCY
If you want to search more versions you can search the USTPO at www.uspto.gov and Arizona at http://apps.azsos.gov/scripts/TNT_Search_engine.dll
Let me know if you have any further questions.