Perhaps Lobelia cardinal is or one of its hybrids?

I have never grown those but I I am familiar with them. Here is some info I looked up so you may propagate many more plants if you like them.

Cut a 6-inch section of lobelia stem that includes two leaves. Take the cuttings while the flowers are still buds. Remove the lower leaf and cut the upper leaf in half with sharp scissors. Dip the cut end of the lobelia stem into the rooting hormone and shake it gently to remove any excess hormone.

Good luck with them.

I read that they need constantly moist soil. Is that correct?

Yes. I would put them in a bright shaded spot so they are not in extreme sun to dry them out. But water them only when they appear to need it and not everyday to create mud. Too much moisture can cause damping off.

You're right, Tim. Lobelia cardinalis does like a consistently moist soil since it is a bog plant native to stream and pond sides. It won't suffer from damping off since that is a condition which affects seedlings at or just after germination.

The OP has been given a well rooted plant rather than a seedling or a cutting.