Delete everything from B:B (including the header) and try this formula in B1:
=ArrayFormula({"Reformatted Name";IF(A2:A="",,TRIM(REGEXREPLACE(REGEXREPLACE(A2:A,"Jr$|Jr.$|Sr$|Sr.$|I$|II$|III$|IV$|Esq$|Esq.$",""),"([^,]+),\s*(.+$)","$2 $1"))&IFERROR(" "®EXEXTRACT(A2:A,"Jr$|Jr.$|Sr$|Sr.$|I$|II$|III$|IV$|Esq$|Esq.$")))})
This formula is written to handle the name cases you've shown and a few additional suffixes. If a name does not fit one of those formats, it should be returned in its original form.
If you find that you run into additional suffixes that aren't already included, just add them to the two lists within the formula, using a pipe symbol |
as the separator.
If you want to change the header text, you will need to do so within the formula itself, not in cell B1.