Trying to avoid a “burner” phone,  but interested in keeping my cell number private.  I know there are several apps available, but wanted to know if anyone had recommendations.  Thanks.

What phone do you have. Most smart phones of the last 3 years or so have the ability to do dual SIM cards. So you can get a prepaid sim and also keep your same phone. So no carrying two phones.

iPhone X.

Just be careful about switching to the wrong the number, as I once did, when texting.

Ah you would need an iPhone Xs and above to use dual sim. But you could also just physically switch the SIM card in and out when you wanted to use the other number. Yea that's a pain but it would serve the same function. If your iPhone is carrier unlocked you can use whatever service you want. Or this may be a reason to look at a new phone now.