Please find below example code and update your customized Publication Type in Tridion.ContentManager.config file and restart SDL Web services.
\tridion\config\Tridion.ContentManager.config
<publicationTypes>
<!--
Constraints:
1) id and name attribute is unique.
2) id > 1024. Numbers below 1024 are reserved.
3) titleResource is optional. if titleResource is not provided then the value specified in name will be used as PublicationType.Title
-->
<add id="1" name="Content" titleResource="lblContentPublicationType" />
<add id="2" name="Web" titleResource="lblWebPublicationType" />
<add id="4" name="Mobile" titleResource="lblMobilePublicationType" />
<add id="5" name="SiteType" titleResource="lblSiteTypePublicationType" />
</publicationTypes>
