How to Rename SharePoint Column Programmatically

Add-PSSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue

$Web= Get-SPWeb "http://sharepoint.company.com"

#Get the "Risk Metrics" List
$list= $web.Lists.TryGetList("Risk Metrics")

#Get "Project Name" Field
$field = $list.fields | where {$_.Title -eq "Project Name"}

#Set Field Display Name and Update
$field.Title ="Program Name"
$field.Update()

           using(SPSite site=new SPSite("http://sharepoint.crescent.com"))
            {
                //Get the "Risk Metrics" List
                SPList list = site.RootWeb.Lists["Risk Metrics"];

                //Get "Project Name" Field
                SPField field = list.Fields["Project Name"];

                //Set Field Display Name and Update
                field.Title = "Program Name";
                field.Update();

                //You can also use: list.Fields["Project Name"].Title = "Project Name";
               //list.Update();                 
            }