How do I automate creating Linodes along with DNS records of the same name?

While you can't automate this in the DNS Manager, you can do it using the Linode API, or even the Linode CLI. Below you can find a sample bash script that does exactly what you're looking for, using the Linode APIv4:

#!/usr/bin/env bash

## Name the Linode/subdomain to be created
TOKEN="YOUR_LINODE_API_TOKEN_GOES_HERE"
LINODE_NAMES=(
    "linode1"
    "linode2"
    "linode3"
)
DOMAIN_NAME="example.com"

## Get the domain's ID from the Linode APIv4
DOMAIN_ID="$(curl -H "Authorization: Bearer $TOKEN" \
        "https://api.linode.com/v4/domains" | jq -S | \
        grep -A 11 "$DOMAIN_NAME" | grep '"id"' | \
        awk '{print $2}' | sed 's/,//')"

## Create the Linodes
for i in "${LINODE_NAMES[@]}"; do
    curl -H "Content-Type: application/json" \
        -H "Authorization: Bearer $TOKEN" \
        -X POST -d '{
        "backups_enabled": true,
        "swap_size": 512,
        "image": "linode/debian9",
        "root_pass": "aComplexP@ssword",
        "booted": true,
        "label": "'"${i}"'",
        "type": "g6-standard-2",
        "region": "us-east",
        "group": "Linode-Group"
        }' \
        https://api.linode.com/v4/linode/instances
done

## Create the subdomain - this assumes your base domain already exists
## in the Linode DNS Manager
for i in "${LINODE_NAMES[@]}"; do
    curl -H "Content-Type: application/json" \
        -H "Authorization: Bearer $TOKEN" \
        -X POST -d '{
        "type": "A",
        "name": "'"${i}"'",
        "priority": 50,
        "weight": 50,
        "port": 80,
        "service": null,
        "protocol": null,
        "ttl_sec": 604800
        }' \
        "https://api.linode.com/v4/domains/${DOMAIN_ID}/records"
done

Note that some of the options for creating a Linode are optional. You can consult the Linode APIv4 Documentation for more information about what options are available, and which ones you do/don't need for your setup. If you have the Linode CLI installed, you can write a similar script that uses that instead. You can also check out our APIv4 Pyhton Bindings if you wish to use Python instead.