Suppose I would like to do business under the name "Biocompumagic", and suppose neither the name biocompumagic nor the name compumagic had been trademarked or ever used in commerce.
What word or words would I want to trademark to make sure that no one else had the rights to the following words in a competing area of interest:
biocompumagic (my name)
Is there any one of these words that I could trademark to de facto prevent use of all four? If not, then what is the least number of words I would need to trademark to ensure that I would have solid legal grounds to use these words?
Any supporting literature/links would be helpful.
(Note: this is a fictious example; trademarks for some of these words do exist, and I am not the holder. I use for illustrative purposes only)