Relational database structure design question

I want to design a relational database to support a dynamic web page for a friend.  The website is about dogs and the database will contain the dog names and all possible competition titles.  I want an end result that allows the user to update the titles (usually multiple titles) a specific dog has earned and then the web page will display the animal's name and all related titles.

I am stuck at having three tables within the DB;
table_DOGS   ---  all dogs breed by breeder
dogs_RegName (PK)
dogs_CallName
<other fields >

table_TITLES  ---  all possible titles
titles_org (PK)
titles_title (PK)
titles_description
<other fields >

table_DogTitles  --  
dogtitles_dogs_RegName
dogtitles_titles_org
dogtitles_titles_title
dogtitles_year

It seems to me I'm creating a many to many situation that I think I don't want.  Is there a better way?