Do I need "the" before the name of my university in the header? [duplicate]

Generally, where a member of a class (the class of all universities) is particularised (say by the addition of "Wroclaw") then you don't need the definite article.

Wroclaw Polytechnic or
Wroclaw University of Technology

will be sufficient for a letterhead. Some insititutions do require the The, but that's a matter of style/affectation which they have adopted.

Where the name of the institution has the determiner/particulariser at the end (as in "University of Sussex") it's normal to use the definite article at the front because there is only one of that particular institution.

The University of Sussex

This applies to including the name in other sentences, too:

I attend the University of Sussex.
I attend Sussex University.

If it were me, I'd put in the "The" (capitalized as I did here. The article is part of the title).

However, you should know that in English (at least in the USA) there is no hard rule here. For example, Oklahoma State Univerity is usually written and pronounced without the article, while Ohio State likes to be a stickler about people using the article: The Ohio State University (I suspect as a backhanded slap at Ohio University).