The entities aren’t saved. They are “generated” every time a component loads them. For HomeMatic you can even pair new devices while HASS is running and they will be directly available. When you stop HASS all entities are forgotten. But the way the entities are generated is static, so f. ex. a thermostat device with the HomeMatic ID MEQ123456 will always get the entity
climate.MEQ123456. That’s why you can use the customization reliably.
This changes if you choose to resolve names. When you do that and the device is named Heizung Wohnzimmer, then the entity ID will be
climate.heizung_wohnzimmer. This usually works fine, although it takes some time to get all these names. And it has one big drawback: if you for some reason change the name on the CCU (f. ex. to HZG Wohnzimmer), then the entity ID will change to
climate.hzg_wohnzimmer, which would break all the customizations, scripts and automations that used the old entity ID.
So yes, if you already have named your devices with name resolving disabled, do not turn it on. The entities the customization depends on aren’t available anymore when you switch. All the resolving really does is renaming the entities to what the CCU has in its metadata. But as stated above, that metadata can change if you choose to rename the device on the CCU. So not resolving + customizing is the most stable and performant choice. Admittedly, you have to deal with the uglier entity IDs in your automations etc., but that’s why I recommended the configurator, which lets you search by the friendly name, but it still adds the correct entity ID to your configuration.