Azure Functions consumption plan naming

You can create a Azure Function on Consumption plan with your choice of name for consumption plan using ARM Template. Below is the sample template and parameter file:

Templatefile.json

{
  "$schema": "https://schema.management.azure.com/schemas/2015-01-01/deploymentTemplate.json#",
  "contentVersion": "1.0.0.0",
  "parameters": {
    "appName": {
      "type": "string",
      "metadata": {
        "description": "The name of the function app that you wish to create."
      }
    },
    "storageAccountType": {
      "type": "string",
      "defaultValue": "Standard_LRS",
      "allowedValues": ["Standard_LRS", "Standard_GRS", "Standard_RAGRS"],
      "metadata": {
        "description": "Storage Account type"
      }
    },
    "location": {
      "type": "string",
      "defaultValue": "[resourceGroup().location]",
      "metadata": {
        "description": "Location for all resources."
      }
    },
    "runtime": {
      "type": "string",
      "defaultValue": "node",
      "allowedValues": ["node", "dotnet", "java"],
      "metadata": {
        "description": "The language worker runtime to load in the function app."
      }
    }
  },
  "variables": {
    "functionAppName": "[parameters('appName')]",
    "hostingPlanName": "[parameters('appName')]",
    "applicationInsightsName": "[parameters('appName')]",
    "storageAccountName": "[concat(uniquestring(resourceGroup().id), 'azfunctions')]",
    "storageAccountid": "[concat(resourceGroup().id,'/providers/','Microsoft.Storage/storageAccounts/', variables('storageAccountName'))]",
    "functionWorkerRuntime": "[parameters('runtime')]"
  },
  "resources": [
    {
      "type": "Microsoft.Storage/storageAccounts",
      "name": "[variables('storageAccountName')]",
      "apiVersion": "2016-12-01",
      "location": "[parameters('location')]",
      "kind": "Storage",
      "sku": {
        "name": "[parameters('storageAccountType')]"
      }
    },
    {
      "type": "Microsoft.Web/serverfarms",
      "apiVersion": "2015-04-01",
      "name": "[variables('hostingPlanName')]",
      "location": "[parameters('location')]",
      "properties": {
        "name": "[variables('hostingPlanName')]",
        "computeMode": "Dynamic",
        "sku": "Dynamic"
      }
    },
    {
      "apiVersion": "2015-08-01",
      "type": "Microsoft.Web/sites",
      "name": "[variables('functionAppName')]",
      "location": "[parameters('location')]",
      "kind": "functionapp",
      "dependsOn": [
        "[resourceId('Microsoft.Web/serverfarms', variables('hostingPlanName'))]",
        "[resourceId('Microsoft.Storage/storageAccounts', variables('storageAccountName'))]"
      ],
      "properties": {
        "serverFarmId": "[resourceId('Microsoft.Web/serverfarms', variables('hostingPlanName'))]",
        "siteConfig": {
          "appSettings": [
            {
              "name": "AzureWebJobsDashboard",
              "value": "[concat('DefaultEndpointsProtocol=https;AccountName=', variables('storageAccountName'), ';AccountKey=', listKeys(variables('storageAccountid'),'2015-05-01-preview').key1)]"
            },
            {
              "name": "AzureWebJobsStorage",
              "value": "[concat('DefaultEndpointsProtocol=https;AccountName=', variables('storageAccountName'), ';AccountKey=', listKeys(variables('storageAccountid'),'2015-05-01-preview').key1)]"
            },
            {
              "name": "WEBSITE_CONTENTAZUREFILECONNECTIONSTRING",
              "value": "[concat('DefaultEndpointsProtocol=https;AccountName=', variables('storageAccountName'), ';AccountKey=', listKeys(variables('storageAccountid'),'2015-05-01-preview').key1)]"
            },
            {
              "name": "WEBSITE_CONTENTSHARE",
              "value": "[toLower(variables('functionAppName'))]"
            },
            {
              "name": "FUNCTIONS_EXTENSION_VERSION",
              "value": "~2"
            },
            {
              "name": "WEBSITE_NODE_DEFAULT_VERSION",
              "value": "8.11.1"
            },
            {
              "name": "APPINSIGHTS_INSTRUMENTATIONKEY",
              "value": "[reference(resourceId('microsoft.insights/components/', variables('applicationInsightsName')), '2015-05-01').InstrumentationKey]"
            },
            {
              "name": "FUNCTIONS_WORKER_RUNTIME",
              "value": "[variables('functionWorkerRuntime')]"
            }
          ]
        }
      }
    },
    {
      "apiVersion": "2018-05-01-preview",
      "name": "[variables('applicationInsightsName')]",
      "type": "microsoft.insights/components",
      "location": "East US",
      "tags": {
        "[concat('hidden-link:', resourceGroup().id, '/providers/Microsoft.Web/sites/', variables('applicationInsightsName'))]": "Resource"
      },
      "properties": {
        "ApplicationId": "[variables('applicationInsightsName')]",
        "Request_Source": "IbizaWebAppExtensionCreate"
      }
    }
  ]
}

Reference: https://github.com/Azure/azure-quickstart-templates/tree/master/101-function-app-create-dynamic

Above answers will help if you are doing using Azure CLI, if you want to do via Portal itself, you can do as follows,

1. On the Azure function Review + create step, there is an option to Download the template for automation and you can click on it. Then the Template will be displayed for downloading.
2. Now click on Deploy
3. Now you can easily change the Hosting Plan Name, agree to T&Cs and click on Purchase.

More Information: http://jaliyaudagedara.blogspot.com/2020/08/azure-functions-consumption-plan-custom.html