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The Dutch surnames databank at www.meertens.knaw.nl describes both Becking and Horsting as place names. Becking is an "old spelling", and appears to be based on the word beek, meaning "stream". Beck and Horst without the -ing ending are both common Dutch place names. Horst may be cognate with the German horst, which is said to have originally meant "brush" or "undergrowth".
I should add that Becking is also found as a surname in Germany, where beck is a dialect word with the same meaning as Dutch beek.