Can I name myself on the Companion Pass? Wife's company pays for flights, I go free?
I've never heard this request before, but it can't hurt to ask Southwest. Just explain it clearly and politely. You never know: it might work.
Might as well wait until funds become non-transferable before you ask. At that time the CR staff will be so swamped with complaints that that they might appreciate the opportunity to do a favor for someone nice.