Dear John, This is a rather large request. The best place to start would be with you great Aunt Fanny.Ask her what she might know about your Cotters. Are you just starting out on your genealogy research?
I did a search in google.com using +"John Redmond Cotter" and found a Vietnam Veteran of that name from Charlotte, Michigan.I would assume he is related to you - perhaps a grandfather?
You might want to ask your local librarian for books on doing genealogic research.There are also great sites online such as cyndislist.com (or it might be .org), ancestry.com, rootsweb.com, as well as genealogy.com were you can find how-to articles on gene research.The National Archives and Records Administration has the US Census reports that are done every 10 years.The 1790-1930 census reports are available to the public at the National Archives, historical societies, and other places.Always ask your librarian for help.The National Archives also has a website.
Remember somethings may not make sense right away but keep at it things will fall into place and you will find who you're named after and much much more.
Look in your phone book for the Family History Center to see if there is one near you.They are very helpful and knowledgable.
I guess you are just starting your research?It takes time but it is worth it.
But, first start with your family and if they aren't willing to talk then keep looking.If you have a local historical society, they might be able to aid you in your search.Of course, you'll have to do alot of the search but when you get more information, you'll be able to ask more specific questions.