Randall Fenwick of Deanham and Hawick (living 1606; d. c.1630), is the son of John Fenwick (b. 1539) of Little Harle. He married Catherine, daughter of Sir Edward Grey of Morpeth and Catherine le Strange.
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They are not too far away, so it's possible Fenwick was from/of either. Or it's possible this is a writing garble over the years.
Deanham is presumably the place in Hartburn, Northumbria: https://www.visionofbritain.org.uk/place/8955
edited by Isaac Taylor
https://www.google.com/maps/dir/Howick,+Alnwick+NE66+3LE,+UK/NE61+4JB,+Hartburn,+Morpeth,+UK/Hawick,+UK/East+Wing+Little+Harle+Tower,+Harle,+Newcastle+upon+Tyne+NE19+2PD,+UK/@55.2979709,-2.4693358,10z/
I'm guessing "Hawick" is a typo, absent better evidence.