I am trying to say the word week but focus on the k sound at the end and really emphasize it. I tend to do this naturally in my everyday speech. It kinda sounds like an odd throat sound when I do it. Is there a name for this?
At a guess (and without a recording it can be no more than that), you are doing one of two things:
If you are merely "overarticulating" the /k/, like an anxious student in a voice production class, you are probably producing a little puff of air when you release the consonant. This sounds like the "BrE" recording on this page, and in IPA it is notated thus: /kʰ/. This is called aspiration; in English it is usually heard only when /k/ starts a syllable and is followed by a vowel, not at the end of a word or before another consonant.
(An unanspirated /k/ before a vowel is often heard among Indian speakers of English; in many subcontinental languages both aspirated and unaspirated stops may appear in this position, and the difference is meaningful.)
If you are really pushing the /k/ it is possible that there is a stretch of time after the release when the tongue is still very close to the palate and air 'hisses' between them. If this is the case you are producing a sound which is not a part of the English phonemic repertory, a voiceless palatal fricative. This is notated /ç/ and is heard in, for instance, German ich, which you may listen to on this page. (Ignore the pronunciation there by Nilreb.)