When a custom search is initiated on the address bar (e.g. when you write "bing.com" on the address bar and hit the Tab key), the address bar starts saying "Search [Label]" (e.g. "Search Bing") where [Label] is the label of the respective custom search.
One can change the labels of the custom search engines from edge://settings/searchEngines (by editing any search engine and changing it in the first one of the three boxes).
However, the change in the label reflected only when you do either of the following:
a) Close Microsoft Edge and restart
b) Change the keyword for the search engine and initiate a custom search with that new keyword, change the keyword back to what it was and initiate a custom search with the original keyword again
Since option b is a thing, I think the change in labels should be reflected immediately, just as if the user had opened a new tab and done all those things, without requiring the user to go through all those hops.