Enström is rather typical of the so-called town names, i.e. used by people like craftsmen, merchants and civil servants (officials) who lived in towns and cities. The common practice for this class of people was to assume a name consisting of two parts which referred to something in nature, very often starting off with a tree.
En-ström is most certainly juniper + stream. Names like it abound in Swedish: Lind-gren (linden branch), Ek-berg (oak mountain), Alm-qvist (elm twig), Ask-lund (ash copse) - and I'm sure a hundred more variations on the theme.
Some regiments gave this sort of town name to its soldiers while others stuck to more typical martial names like Spjut (javelin) or Lans (lance) or even Krig (War)! But soldiers' names were not supposed to be retained by a soldier after he was discharged, and it was very rare before the mid to late 19th century for a soldier's family to use his soldier name. The soldier name can be viewed more along the lines of a badge of office.
So while is is entirely possible that your Enström ancestor was a soldier and that was how the name was acquired, it is much more likely that the origin of the name lies with some craftsman (shoemaker, cabinetmaker etc) or tradesman/merchant.
Ingela