For example "Tomb Raider III - The Lost Artifact (Europe)" uses the USA spelling and not artefact. This is for the easier search rule? But then if you search for center and centre you will get different results. Also honor and honour. And they might be more.

Maybe keep the authentic name but use the US spelling as an alternative for the search engine in european games?

Depends on where the game was issued and if the text is actually changed IMO. Sonic Colors (US) vs. Sonic Colours (PAL region) is another example.

Technically it shouldn't be too hard to implement as long as there is a word list to tell the search engine to display all word variants. Type 'colors' and it should search for both 'colors' AND 'colours' unless someone puts it in double quotes e.g. "colors" to force it to only search for that particular string.