Names that can be used are very hard to find. For example, if a streaming station in New Hampshire wants to call itself "The Rat" and registers it as a national mark and is listenable in Idaho, nobody in that state can use the "Rat" name there. So finding names that are unencumbered is very hard now.What I don't understand is why radio companies don't try to find more unique names for their stations in this age of online radio. Just looking at Seattle and Portland for instance, there are two stations called 99.5 The Wolf, one in Portland and one in Dallas. There are also two Z100s, Portland and New York. This was prior to smart speakers so it may not be relevant, but there were 3 K103FMs at one point. These were Portland, Centralia/Chehalis, and Spokane. Looking at Seattle, there was another station with a Classic Hits format in Arkansas that until recently was using the name Star 101.5. When 106.1 in Seattle was still known as Kiss, it shared a branding with two other stations, one in Dallas and one in Evansville. I almost forgot about 102.9 Now, which was patterned and imaged after Dallas. And that's just the Seattle and Portland markets. Zoom out to the entire country and there are many more.
And once a company has a name that they own, they will use it over and over. Or when a name never got registered nationally and there are lots of different users, others will pick it up in unused states or areas.