You have multiple solutions, I will give you some and case uses of.

Bash

Situation 1: You only change server name (and possibly document root).

You can make script that write file from scratch or write template, copy it with desired name and change needed parameters.
Let's say we will go with template.
I will create template in /etc/nginx/sites-available/template:

server {
        listen 80;
        listen [::]:80;

        root _;
        index index.html index.htm index.nginx-debian.html;

        server_name _;

        include snippets/example.conf;
}

I will make script that takes two arguments: server name and document root. It will copy template to srvname.example.com and script will execute sed command to update values. sed (stream editor) is very powerful command-line text editor, it can be used to update values in files and much more. You can learn more use cases in sed GNU docs.

#!/bin/bash

domain=$1
root=$2

cp /etc/nginx/sites-available/template /etc/nginx/sites-available/$domain

sed -i -e 's/server_name _/server_name '$domain'/g' /etc/nginx/sites-available/$domain
sed -i -e 's/root _/root '$root'/g' /etc/nginx/sites-available/$domain

ln -s /etc/nginx/sites-available/$domain /etc/nginx/sites-enabled/
systemctl restart nginx

Explanation:
We used here Bash command-line arguments. When you call script with ./script.sh x y you can get x and y by $1 and $2.
First sed will try to find server_name _ and change it to server_name $domain.
Second one will do the same but now for root In case you don't need it, you can just remove that line and root=$2 line.
ln will create symbolic link to sites-enabled which will enable your site.

This is easiest solution. I can write you script that will make config from scratch but I think template will be best.

About Ansible. It's configuration management system. Follow link to learn more about it, you can also take a look at Ansible tutorial by Erika Heidi.

If you need more help, feel free to ask, I will try to help you :)