I like to start by visualizing the sign. Since my world trends fairly medieval, I assume that most people don't read. That means that the sign needs to be graphic.
Some of the signs are painted and two-dimensional; some are carved into three-dimensional shapes. Two that I like:
The Brass Tankard, whose sign is crudely painted on a rough board, is known to most as "The Brazen Drunkard". (The clientele isn't, shall we say, exclusive.)
The Gilded Unicorn, a higher-class place, has a carved rampant unicorn with gold paint. But some years ago an ejected drunk took offense at being bounced and took some revenge on the sign. The bar is now usually referred to as "The Gelded Unicorn".