This shows the Charles Street facade of the pub. Since the photograph was taken the pub's name has been changed to the Nelson Public House. The colour of the paint has changed too - it is now a rather unattractive dark grey. The references to Admiral Lord Nelson have disappeared in the repaint.
The elephant and castle is the original name for this pub and goes back at least as far as 1880 when it was a humble beerhouse. The name of Simple Simon was coined in the 1970s and was linked to the Shires pie factory that was close by. The Elephant and Castle most likely refers to the coat of arms of the City of Coventry