Since `BuiltinData` derives `Show`:

```
newtype BuiltinData = BuiltinData PLC.Data
    deriving newtype (Show, Eq, Ord)
```

and there's the function:

`stringToBuiltinString :: String -> BuiltinString` found here in `PlutusTx/Builtins/Class.hs`

Assuming your "variable name" is `dummyBuiltinData`, you can convert `BuiltinData` to `BuiltinString` using:

`stringToBuiltinString $ show dummyBuiltinData` 

EDIT:

As noted by [kolam](https://cardano.stackexchange.com/users/2681/kolam), `show` isn't `INLINABLE` and isn't applicable on-chain. Here is a version that should work:

`decodeUtf8 $ unsafeDataAsB dummyBuiltinData`

both `decodeUtf8` and `unsafeDataAsB` can be found in module `PlutusTx.Builtins.Internal`