Interesting point. I think many historical pub names pre-date general literacy and many folk depended on signs to locate different trades and businesses. The pub signs we see nowadays are a survivor of signs which were more common and seen outside other premises.
Usually the sign of the Swan related to the Earls of Leicester and the Red Lion was a Lancastrian symbol. Over the years the names stuck and as the use of Welsh declined the names of the pubs were added in English, especially with the advent of tourism in the 19th C. This was so even in very Welsh speaking areas.
In the 19thC, Glan Conwy boasted several small pubs but all had English names despite the fact the majority of the population were Welsh speakers. Examples include, The Crown, The Britannia, The Prince of Wales.