The thesaurus may help, depending on the various sentences.
http://thesaurus.reference.com/browse/become
However, you'll probably do better to isolate each usage of these words and work on rephrasing the entire idea or sentence. If you want further help on this, be sure to post your whole paper.
In my 5-paragraph essay, I say "my goal of becoming a doctor" or "to become a doctor" at least 4 times. What can I say instead of become?
2 answers
How about "my career" or "my goal," since you have already specified that you want to be a doctor?