St. James' Park is the correct way to show it. St James's Park is
incorrect.
Its like; I'm going to Chris' House, not I'm going to Chris's house

I think this is an area that can cause much debate. A quick internet search
suggests a consensus for using an apostrophe and an s unless the word sounds
ugly with it and that is certainly how I use it.

I would certainly say Chris's house and I would generally say St James's
Park, just as I would say princess's or Thomas's. However many would find
Thomas's ugly and just use Thomas' (as in St Thomas' Hospital). Sometimes I
do myself and I will sometimes say St James' Park when it trips off the
tongue better.

However regardless of any of that St James's Park is the accepted correct
name for the park. On the other hand it seems Newcastle play at St James'
Park and Exeter City at either St James Park or St James' Park depending on
if you read The Guardian or The Times.