I’m getting a new phone next month and was wanting to put it on that phone when I get it.
Most likely, yes. At the very least, you will be able to use cloud names on the new phone.
If you are keeping the same OS (Android > Android or iOS > iOS) you can do a backup and restore that backup to your new phone to keep your single player worlds and portal chest contents.This should also keep your support ID so you can continue to use your names on cloud worlds, but if it doesn’t, you just have to message Milla and ask her to merge your new and old support IDs.
If you are switching OS (Android > iOS or iOS > Android) you will be able to message Milla to ask her to merge your support IDs so that you can use the same names when playing on cloud worlds. You won’t (without a difficult process, which doesn’t have a guide yet) be able to transfer your worlds or portal chest contents.
If you’re using iOS, do an iCloud backup and use that backup when setting up your new phone.