The "ye" in Ye Olde Bookshop and other mildly nauseating names isn't - and never was - pronounced "ye". Our ancestors pronounced it "the".
So why write "ye", ye ask (that second one was the nominative "ye", as in "O, ye of little faith"). I'll tell you. The letter "y" was a printer's adaptation of an Old English character called the thorn, used to represent the "th" sound. It looked like this: þ. "Y" was allegedly the nearest character available in the Roman alphabet, which makes you wonder if our forebears had ever seen the letters b or p.