Make wildcard subdomain redirect to other domain and copy subdomain

I have a domain ex: mydomain.com. Using a wildcard subdomain ex. name.mydomain.com users can refer to this as their homepage. It will be many users:

name.mydomain.com
name2.mydomain.com
name3.mydomain.com
names4.mydomain.com
myname2.mydomain.com

When someone go to that URL, it should:

1. Redirect to this other domain I have: otherdomain.com
2. Attach the subdomain after domain ie. if subdomain is "name1" = otherdomain.com?name=name1

Understand?