Is there a way to combine VertexLabeling->True and VertexLabels/Tooltip in TreePlot?

Basically, I'm trying to make Mathematica give me a tree with names inside the rectangles like so:

...while also having the properties of VertexLabels or Tooltip, which lets me place my mouse over the name in the rectangle to give me additional information. Using VertexLabels alone places the names outside the nodes, which I don't want. Nor do I want circles - they need to be rectangles. Tooltip alone doesn't seem to work for the nodes, only the edges. Any help will be much appreciated.

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ttF = Tooltip[#, "The Iliad of Homer"] &;


Use "The Iliad of Homer" as the tooltip for the nodes and the edge:

TreePlot[{ttF[# -> #2] & @@ ttF /@ {Peleus, Achiles}},  VertexLabeling -> All]


Alternatively, (1) Use the syntax $\left\{\left\{v_i\to v_j,\text{lbl}_1\right\},\ldots \right\}$ instead of $\left\{v_i\to v_j,v_{2 i}\to v_{2 j},\ldots \right\}$ to specify the edges. (2) Use the option settings VertexLabeling -> All and EdgeLabeling -> Automatic. (3) Post-process the TreePlot output to change the Tooltip labels.

TreePlot[{{Peleus -> Achiles, ""}}, VertexLabeling -> All, EdgeLabeling -> Automatic] /.
Tooltip[v_, _] :> Tooltip[v, "The Iliad of Homer"]
(* same picture *)