Suddenly indexed as www.theme.example.com

Never made a link with www

[jetteroheller]

I have my main domain with several subdomains named by the theme.

They are all without www.

No I found out, that one of my subdomains is
suddenly listed at Google as

[theme.example.com...]

How can this happen

[g1smd]

Simply because your website serves pages at that URL, and serves them with a 200 OK status - and Google found them from some link that included the www.

I would go with that and set up a 301 redirect from non-www to www so that they only "see" one site. If they get to see the non-www version then you will have a lot of problems, and they will take several years to clean up.

[tiori]

check your dns records. You might actually have an entry for "www.theme.example.com" that was created when you added your subdomains.

[jetteroheller]

At my web provider, all domains are with and without www equal to reach.

The subdomain was created 2002.

All the years indexed by Google without "www"

[g1smd]

It only takes one wrong inbound link for your site to start having lots of problems.

Make sure you fit that 301 redirect from non-www to www and you will never have a problem.

It takes 5 minutes to set it up and test it.