By custom, a wife who chooses to take her husband's name as a result of marriage does not need to go through a court proceeding to change her name. This may be accomplished by notifying the appropriate agencies. by way of example, a wife should record her new name with Social Security, her employer, the IRS, the Bureau of Motor Vehicles, the Board of Elections, the school she attends or has children attending, credit card companies, and all financial institutions in which she has accounts.
The husband may adopt the wife's name and the parties may hyphenate their name. However, since these changes are not common, they may be more difficult to accomplish. The parties may need to file a legal name change by filing an application for name change in the Probate Court of the county of residence for the past year and meeting other statutory requirements.

Employers should be notified of the change in marital status. If appropriate, the married couple should adjust their federal and state income tax withholdings and the beneficiaries of any retirement plans or Insurance Policy Some contracts, divorce decrees, and domestic court rules require notice of the change in the marital status. Such documents should be reviewed to determine if notice is necessary. If either party changes their residence address, the Board of Elections in the county of the new residence should be contacted.

Individuals should be aware of the existence of nongovernmental agencies claiming to change social security and/or credit card information for a nominal fee. This Court does not endorse such services. This can be accomplished at no charge by directly contacting Social Security and other entities.

The above information was found on the Franklin County Probate Court site