Copy names in B downward as long as A is the same

Ok here's what I need. If column B has a name in it, and the cell to the left of that name has a number (i.e. 2114) I need the name in the initial cell in column B copy/pasted into every cell in B as long as the 2114 is in the cell to the left in column A.
I've provided a picture to show a bit more of what I'm talking about, as this is genuinely confusing me.
There are a lot of names in B, most unique, but the corresponding number to the left of those names is the deciding factor of whether the names are copied into the corresponding cells to the right of that same number.
Sorry if this is a choppy way of explaining my situation. Please feel free to ask questions.Screen Shot 2019-02-16 at 5.04.07 PM.png

NOTE: I [I]was[I] doing this manually, which is why the only real example is at the top, numbered 1-1876 with the corresponding name Cindy Lee Brooms.

Well a really quick way would be to filter on Column A by that number then paste and fill down.