how to delete all names on the map

You need to use a map style that doesn't display names, there used to be such layers available but they don't seem to be available any more, see https://help.openstreetmap.org/questions/1873/how-can-i-create-a-map-without-any-names-on-it

As a result you probably will need to create you own style without names. This is fairly simple but how to achieve it best depends on what you want to end up with, for example with a raster tile or vector tile based web map, or maybe something else.

To be clear do not try to delete names from the data, this will only get you in to trouble.

Carto has a basemap without labels to offer, see https://carto.com/help/building-maps/basemap-list/ , e.g. "Voyager without labels" or Positron without labels or Dark Matter without labels.

You'll need an api key to use those tiles. Non-commercial use is regulated by these terms: https://go.carto.com/hubfs/CARTO-Free-Basemaps-Terms-of-Service.pdf