If you have always held separate accounts then you do not need to close them and reopen new ones. The money in the accounts is considered marital property to the date of separation. Example: You have $500 in the checking account and separation begins today. You get paid next week. That $500 is marital property and would be divided. When you get paid next week, that money is separate property.
If you are on this step then you and your spouse should sit down with and come up with a separation agreement detailing these accounts. If you and your spouse are going to keep the money in the separate accounts and not divide it then it needs to be disclosed that way in an agreement to keep from one or the other coming back later for it our of spite.
If you have joint accounts, you should separate them to ensure that your assets after separation are not being divided along with marital assests. I have read of one couple that kept a joint account open for child support and/or alimony…but you would need to have an agreement and a healthy communication and respect for one another to be able to do this after divorce, IMHO.