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create a custom field for the real name

In ACP >> User Profile Fields >> Add New Profile Field >> Single Line Text Box

Make a note of the profile field ID.


In Postbit / Postbit Legacy Template, find

PHP Code:

<a class="bigusername" href="member.php?$session[sessionurl]u=$post[userid]">$post[musername]</a> 


Add Under:

PHP Code:

<if condition="$post['fieldXX']">$post[fieldXX]</if> 


Replace XX with the field number from before.