You don't need a name.com login to verify your domain. For Google Search Console, choose the TXT record verification method instead of the domain registrar method. Open your domain at railway.com/workspace/domains and you'll see a DNS records table. Add the TXT record Google gives you (type TXT, name @, and paste the verification value), save it, wait a few minutes for propagation, then run verification in Search Console.

what should be the TTL then?

Any value works for verification records. 300 (5 minutes) is a safe choice if the form asks for one, but Google Search Console only checks that the record exists, not its TTL.

i am trying but still failed. It says that google cant find txt in dns record

Google not finding the record usually means it either wasn't saved or needs more time to propagate. Open your domain at railway.com/workspace/domains and confirm the TXT record appears in the DNS records table with the name set to @ and the value being the exact verification string from Google Search Console. If it is already there, wait 5-10 minutes and retry verification.