It seems they are not real clear with the name change
In September, 2020, they said
The flagship Lumen brand is targeted toward larger enterprises, the likes of which would be most likely to adopt the company?s most advanced services.
The CenturyLink brand is being retained for legacy copper services delivered to residential customers and some SMBs, as well as existing FTTH customers.
The CenturyLink name will only be associated with residential and small business customers served by copper networks. ?CenturyLink, with its strong heritage, will remain as a trusted brand for residential and small business customers over traditional networks,? the company said.