Get alternative elements in JSON using JQ (output: JSON object)

I have a problem where I'm receiving JSON that depending on the source, may have some data at root level or under another element.

From this JSON I need to extract multiple elements into a nother, normalized JSON, with custom keys for the values.

Sample JSON 1:

{"name":"John","last":"Smith","position": "clerk"}

Sample JSON 2:

{"personData": {"name":"John","last":"Smith"}}

I was using this at the beginning as all my test jsons had the first form:

jq '{nombre: .name, apellido: .last, puesto: .position}'

When they started coming up empty I tries using the // operator but it doesn't seem to work if I'm providing the keys:

Doesn't work:

jq '{nombre: .name//.personData.name, apellido: .last, puesto: .position}'

Works (but I don't get any keys):

jq '{nombre: .name//.personData.name, apellido: .last, puesto: .position//null}'

I've never had to use jq with conditionals or logic like this, so I may be missing something obvious.
(actual json files are pretty extensive and whichever logic I need to use will end up applied to a dozen or so fields, so I'm looking for a sustainable solution.

Expected output would be for the first sample:

{"nombre" : "John", "apellido": "Smith", "puesto": "clerk" }

And for the second sample:

{"nombre" : "John", "apellido": "Smith", "puesto": null}

Answer:
Ended up using this style, which allows for searching in multiple blocks for extracting multiple data:

(.personData // .) + (.addressData // .) | {nameValue: .name, streetValue: .streetName }

(simplified: The .name value can be at root or under .personData.name, and the .streetName value can be at root or under .addressData.streetvalue, so the above normalizes the situation for both blocks into the same stream)

One of many possibilities:

(.personData // .) |  {nombre: .name, apellido: .last, puesto: .position}

If you want a fully exhaustive search for all JSON objects with .name, then you could use .. or walk/1. If you want at most one such object, you could use first/1, which might be a good idea anyway as it might speed things up.

One way, using recursion ..:

.. | select(has("name") and has("last"))? |
    { nombre: .name, appelido: .last, puesto: .position }

Can be re-used in other contexts.

From man jq:

> Recursive Descent: ..
> Recursively descends ., producing every value. This is the same as the zero-argument recurse builtin. This is intended to resemble the XPath // operator.