Abarim Publications' online Biblical Hebrew Dictionary
The two forms אסם ('sm) and סנה (snh) have nothing to do with each other, yet there is some overlap in form and similarity in meaning:
The root אסם ('sm) means to gather or store. It doesn't occur as verb in the Bible, and only one derivation remains: the masculine noun אסם ('asam), meaning storehouse (Deuteronomy 28:8 and Proverbs 3:10 only). However, BDB Theological Dictionary lists the Aramaic equivalent of this noun, namely אסנא ('sn'), and then proceeds to discuss the name Asnah, which is spelled אסנה (asna; Ezra 2:50). It isn't clear whether BDB suggests that Asnah comes from the root אסם ('sm), but BDB does propose that this name Asnah is the equivalent of an Aramaic name that's spelled אסנא ('sn'), and which means thorn-bush, which brings to mind the following word:
The masculine noun סנה (seneh) denotes a kind of bush, namely the bush that famously burned when God addressed Moses from it (Exodus 3:3). HAW Theological Wordbook of the Old Testament states, "the botanical identification is uncertain as is the derivation," but lists as one of many suggestions the common shittim or acacia tree (שטה, shitta). BDB Theological Dictionary is more confident and declares the seneh to be typically a thorny bush, like a black berry bush. This confidence apparently stems from a look at equivalents in the cognate languages. In 1 Samuel 14:4 occurs the name Seneh, which is identical to the word for our bush, and BDB Theological Dictionary calls out, "(= thorny . . . )".