If at all possible, you want to avoid doing any kind of programmatic manipulation of people's names. If it's important for you to have separate First, Middle and Last name fields, the user should fill those out themselves, rather than you trying to extract them. If you've never read https://www.kalzumeus.com/2010/06/17/falsehoods-programmers-believe-about-names/ it's worth a look. The approach you've outlined will end up with last names like "Jr." and "IV" given reasonable inputs - and that's if you remember to allow periods in your regex. I regularly receive mail addressed to "Keever, Brian Mc" - and I *never* write my name with a space!

All that said, sometimes you don't get to dictate the requirements. Making the fewest assumptions you can here is important. Spaces separate names, and anything else is part of a name. So you want something like:

([^\s]+)\s([^\s].*?)?\s?([^\s]+)

\s is a space character, so ^\s is part of a name. This assumes there is only 1 space between names, if that's not true you'll need to adjust to account for it.