I found the solution. Inspired by this post:
http://www.xml-convert.com/en/convert-tff-font-to-afm-pfa-fpdf-tcpdfWhere I read that the naming of the bold font should be with just an"i" after the name and not "it" as I did. I copy part of the post:
[basic-font-name-in-lowercase].php for regular font
[basic-font-name-in-lowercase]b.php for bold variation
[basic-font-name-in-lowercase]i.php for oblique variation
[basic-font-name-in-lowercase]bi.php for bold oblique variation
So basically the wiki information could be made much simpler to understand, at least for Windows users:
Copy the font you want to use from the Windows/fonts folder to folder where you can read and write without trouble (I copied to a folder on my desktop).
Go to this site
http://www.xml-convert.com/en/convert-tff-font-to-afm-pfa-fpdf-tcpdf and enter the filename respecting the indications on the top of this post (lowercase, file name endings).
Copy the resulting files to the html2pder/tcpdf/fonts folder.
Without any changes of config files or other, I got Trebuchet MS to work with HTML2PDF in normal, bold and italic font.
I don't know how to change the topic to "solved"? Admin, please help ;-)