What would an AST (abstract syntax tree) for an object-oriented programming language look like?

AST is an abstraction of the CST (concrete syntax tree, or, parse tree). The concrete syntax tree is the tree resulting from the productions (in the grammar) used to parse the file. So your AST is basically derived from your grammar definition, but has for transformed

                        Exp                    
                      /  |  \                   
                     /   |   \                       *
                 Ident BinOp Ident       into       / \
                  /      |     \                  "x" "y"https://stackoverflow.com/"      \
               "x"       *      "y"

All in all I think the example in your post looks fine. I would probably wrap the variable declarations in a varDeclList and the function declaration in a methDeclList, and the return statement in a stmtList. (See below.)

One more or less “real” representation of an AST is described by Apple in his book “Modern Compiler Implementation in Java”. (Resources can be found here.)

Using those classes, your program would be represented as follows:

Program
    ClassDeclList
        ClassDecl
            Identifier
                id: Person
            VarDeclList
                VarDecl
                    type: String
                    id: name
                VarDecl
                    type: int
                    id: age
            MethDeclList
                MethodDecl
                    modifiers: public
                    returnType: String
                    id: toString
                    Formals
                        (empty)
                    StmtList
                        returnStmt
                            Identifier
                                id: name