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Nyquist
Swedish: ornamental name composed of the elements ny ‘new’ + quist, an old or ornamental spelling of kvist ‘twig’.

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On Trenk ...just an educated guess ...

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Trench
English and Scottish (of French origin): habitational name from La Tranche in Poitou, so named from the Old French topographical term trenche, a derivative of the verb trenchier ‘to cut’, which denoted both a ditch and a track cut through a forest. The term is also found in Middle English, and in some cases the surname could be of topographic origin or from minor place, such as The Trench in Kent, named with this word.

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Now with Semchee, I may need a bit more help. Do you know the country of origin? I looked each syllable up separately as I didn't find anything for the entire word. Here's what I got ...

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German: metonymic occupational name for a beekeeper, from Middle High German seim ‘honey’.
Norwegian: habitational name from any of ten or more farms so named, notably on the west coast of Norway, named with Old Norse Sæheimr, a compound of sær ‘sea’ + heimr ‘home’, ‘farmstead’.

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chee
Navajo: unexplained.
Chinese: variant Romanization of Qi.
Korean: variant of Chi.
Dictionary of American Family Names
Sem
Norwegian: habitational name from any of about fifteen farms so named, a variant of Seim.
Slovenian: from the medieval personal name Sem, a shortened form of Simon.
Cambodian: unexplained.
Indian (Panjab): Hindu (Saraswat Brahman) name of unknown meaning.
Seim

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Anyway, it’s the best I can do with the info you've given …

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