As we have mentioned many times, Ernie, Russian Jews were first assigned
permanent family names in 1826-but they didn't use them. Your ancestor was
still Abraham ben Isaac or whatever.
The government wanted to keep track of the family so it would know who was
draftable (often the first son was exempt) and who was allowed to marry
(legally that is, sometimes only the oldest son was allowed to marry) and
who was taxed. All of these are good reason for Abraham ben Isaac to
confuse things and not use the name he was signed up with. Over the years,
of course, we see that the surnames were used in different events registered
by the government-births, marriages, deaths-and often the names varied for a
long time before they became set. In your case, I would guess that the name
was used in a different form Bakstansky or Baksht.
Now, the challange for someone else, Baksht sounds to me like it might be
the acronym of some famous rabbi, but Dan Rottenberg doesn't have that
meaning for it. If this is true, it might have been turned into a 'Slavic'
form by adding the -ansky. Or else it might have been a town name. I am
certainly not an expert on famous rabbinical names. But I would think the
two names are just alternate forms of the same thing.
People didn't usually change their names because of the death of a spouse or
anything like that with one exception: sometimes if a man married a woman
who's father had no sons, he might take that man's surname-to become
undraftable(?) or just to perpetuate the name. Your two versions seem too
similar for that, but it is possible.