You’ll need to change both formats, and because your note name doesn’t include all the date information required to construct a date (it’s missing the year), we’ll need to get that date information from the path.
[[<% moment(tp.file.path(true), '[8 History/Daily Journals]/YYYY/MM/DD-MMMM ddd.md').add(1,'days').format('[8 History/Daily Journals]/YYYY/MM/DD-MMMM ddd|DD-MMMM ddd') %>]]
Note that I also added [[ and ]] to the beginning and end to make it a link, and added |DD-MMMM ddd to add an alias, so you don’t see the full path in live preview and reading mode, just the note name.
Also note that this solution is tightly coupled to your daily note settings, if you change them, you’ll need to change your template as well. There are ways to dynamically retrieve those settings if you wish, for example:
<%*
// Retrieve daily note settings
const { folder, format } =
app.internalPlugins.getEnabledPluginById("daily-notes").options;
// Define the format of the path to a daily note
const pathFormat = `[${folder}]/${format}`;
// Define the display text format
const aliasFormat = format.split("/").at(-1);
// Define the date based on the path of the current file
const today = moment(tp.file.path(true), pathFormat);
// Generate the link
const nextDailyNoteLink = "[[" + today.add(1, "days").format(`${pathFormat}|${aliasFormat}`) + "]]";
-%>
<% nextDailyNoteLink %>