Can I override the author name abbreviation in the abbrv bibliography style?

So I found a solution myself: \mbox{Th.} in the bibliography. Better answers are welcome of course.

You wrote at the end of your own answer:

Better answers are welcome of course.

I would like to suggest that you set up the author field as

author = "{\relax Th} Author",

rather than as author = "\mbox{Th.} Author",.

What's the practical difference, you may ask? Won't either approach render the first name as "Th."? The answer is no, at least not under all circumstances

Suppose that one day, you choose to -- or are required to -- use a bibliography style that truncates first names but does not affix a "." (period, full stop) to the initial. In such a case, the \relax-based method correctly gives "Th", whereas the \mbox-based method will continue to produce "Th." -- contrary to what the bibliography style calls for. It's convenient not to have to edit the bib file when one switches the bibliography style, right?

For more information on the subject of how one should enter first names so they're abbreviated to more than just the first letter, see the posting BibTeX: abbreviate name to 2 or 3 letters (not 1)