Hello Daniel Andryszak
To renew or issue certificates for others using a single Windows Server CA, you need admin rights and a certificate template that grants "Enroll" and "Autoenroll" permissions to the target users or groups. Use the Certification Authority MMC or the certreq tool with a valid request file to generate certificates.
If you're logged in as yourself, renewals apply to your account. To create certificates for others, either log in as them or use a certificate template with a CA-signed request. After issuing, export the certificate (with or without the private key) and deliver it securely.