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So I want to be able to put axes labels simultaneously as the numerical labels.

I can achieve that with the following, but is there a better/cleaner way? I can't use callout, because I am using version 10.4.0 for Microsoft Windows (64-bit) (February 26, 2016)

names = {cat, dog, monkey}
data = {7,12,3}
BarChart[data, ChartLabels -> names , 
 BarOrigin -> Left, ScalingFunctions -> "Log", AspectRatio -> 2, 
 LabelingFunction -> (Placed[Row[{"$", #}], After] &)]

enter image description here

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Not necessarily better/cleaner than your approach but you can also add multiple labels using the option ChartLabels only:

BarChart[data,
 ChartLabels -> Placed[{names, Row[{"$", #}] & /@ data}, {Axis, After}],
 BarOrigin -> Left,
 ScalingFunctions -> "Log",
 AspectRatio -> 2]

enter image description here

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