Update 2: Came across a hidden option "VertexNames" for TreePlot
TreePlot[{1 -> 2, 1 -> 3},
VertexLabeling -> True,
"VertexNames" -> {"A", "B", "B"}]

This also works for GraphPlot and LayeredGraphPlot.
Note: In versions 12.0, TreePlot is changed substantially, and the legacy Treeplot is available under the name GraphComputation`TreePlotLegacy.
Update: If you have to use TreePlot you can post-process the output of TreePlot to relabel the vertices.
The function reLabelF below takes a list of vertices to be relabeled (vertices) and their new labels(labels) and post-processes a TreePlot output (tp) to get a relabeled TreePlot:
ClearAll[reLabelF]
reLabelF[verts_, labels_][tp_] := tp /. (Framed[#, p__] :> Framed[#2, p] & @@@
Transpose[{verts, labels}])
Examples:
vertices = {1, 2, 3};
labels = Style[#, 18, "Panel"] & /@ {"a", "b", "b"};
TreePlot[{1 -> 2, 1 -> 3}, VertexLabeling -> True] // reLabelF[vertices, labels]

Relabel only the vertices {1, 2, 3}:
TreePlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 5}, VertexLabeling -> True] //
reLabelF[vertices, labels]

Relabel all vertices:
TreePlot[{1 -> 2, 1 -> 3, 1 -> 4, 2 -> 5}, VertexLabeling -> True] //
reLabelF[Range[5], Style[#, 18, "Panel"] & /@ {"a", "b", "b", "b", "c"}]

Original answer:
You can specify the labels for each vertex using Property and use the built-in "VintageDiagram" for GraphStyle option setting:
labeledvertices = Property[#, VertexLabels ->
Placed[Style[#2, 18, "Panel", Background -> Transparent], Center]] & @@@
Transpose[{{1, 2, 3}, {"a", "b", "b"}}];
TreeGraph[labeledvertices, {1 -> 2, 1 -> 3}, GraphStyle -> "VintageDiagram"]

Alternatively, use a different built-in GraphStyle:
TreeGraph[labeledvertices, {1 -> 2, 1 -> 3}, GraphStyle -> "DiagramGold"]

TreePlotwhen you already have the correct layout fromTreeGraph? You can just re-style the TreeGraph using EdgeStyle, VertexStyle, Placed in VertexLabels, VertexShapeFunction, etc. See the documentation for each of these. – Szabolcs May 11 '17 at 08:43