The certificates are stored in policy store with a unique ID. When the cert is used with Federation Partnership, the certificate's Xid is used to link the two objects together. Hence, manually changing the alias is not going to update the certificate that has been included with the Federation Partnership.
Example:
<Object class="CA.FED::Certificate" Xid="CA.FED::Certificate@090395dc-7096-4298-9acf-a26a018788c8" CreatedDateTime="2015-12-02T02:05:33" ModifiedDateTime="2015-12-20T23:50:51" UpdatedBy="siteminder" UpdateMethod="GUI" ExportType="Replace">
<Property Name="CA.FED::Certificate.FIPSApproved">
<BooleanValue>true</BooleanValue>
</Property>
<Property Name="CA.FED::Certificate.Type">
<NumberValue>2</NumberValue>
</Property>
<Property Name="CA.FED::Certificate.SerialNumber">
<StringValue>6173ca55000000000003</StringValue>
</Property>
<Property Name="CA.FED::Certificate.Alias">
<StringValue>saml2sign</StringValue>
</Property>
<Property Name="CA.FED::Certificate.IssuerDN">
<StringValue>CN=KellyRoot,DC=kelly,DC=lab</StringValue>
</Property>
<Property Name="CA.FED::Certificate.CertificateGUID">
<LinkValue>
<XID>CA.CDS::Certificate@c28eb650-1b20-4a9d-8008-03ca353598c4</XID>
</LinkValue>
</Property>
</Object><!-- Xid="CA.FED::Certificate@090395dc-7096-4298-9acf-a26a018788c8" -->
<Object class="CA.FED::PartnershipBase" Xid="CA.FED::PartnershipBase@7412f90b-0b88-4dc4-bb3b-bcff177f41f4" CreatedDateTime="2015-07-29T02:16:27" ModifiedDateTime="2015-12-02T02:43:29" UpdatedBy="PRODUCT: CA.FED LIBRARY: FedObjects" UpdateMethod="Internal" ExportType="Replace">
.......
<Property Name="CA.FED::PartnershipBase.SigningCertLink">
<LinkValue>
<XID>CA.FED::Certificate@090395dc-7096-4298-9acf-a26a018788c8</XID>
</LinkValue>
</Property>
........
</Object><!-- Xid="CA.FED::PartnershipBase@7412f90b-0b88-4dc4-bb3b-bcff177f41f4" -->
I'm not sure bout CloudMinder, but you can do a policy export and check the references.
Also, with Single Sign-On Policy u, we have the option to update the existing certificate via Administrative UI.