Hi Enqnety, Welcome to English Forums. In your sample sentences, 'Head' without 'the' is OK if it is capitalized, since it would be Monica's title; so both sentences are possible. Explaining all the uses of 'the/a' and when they are omitted is a complex subject, and I suggest that you first use Google to search 'definite article' and 'indefinite articles', and then come back here with more specific questions.
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