Usually, when you create a new site collection, you enter the samaccountname (domain\username) of the user as primary site collection administrator

What you should do, if your farms are using the SAML based authentification. You have to declare the type and value of the claim

Let’s take the claim “User Principle Name” (UPN)

$claim = New-SPClaimsPrincipalClaimValue “<name.surname@domain.com>” ClaimType http://schemas.xmlsoap.org/ws/2005/05/identity/claims/upnTrustedIdentityTokenIssuer “Trusted_Identity_Provider_Name”

$template = Get-SPWebTemplate “<Template_code>”  #  ex: STS#0

New-SPSite -Url “<url_site_collection>” OwnerAlias $claim.ToEncodedString() -Template $template