Is there any word for the strap of the bra that is visible on shoulder.?
Mostly it is addressed as strap which is obviously a common word not specific to bra or any inner-wear.
It is simply called a bra strap
In the US (and elsewhere), current fashion often allows bra straps to show. In earlier eras, such a display might have been considered a peekaboo style
Now, almost anything goes (maybe even a glimpse of stocking).