Is it safe to use the name for our Application?
YouTrack is a registered trademark of another company producing software.
Said software is 14 years old, so there is no question here of who came first.
The trademark is valid in the EU. In Germany specifically, this is covered by MarkenG.
You using the same name for your software as the one registered as a trademark for their software goes against many of the points, but the most obvious one is
(2) Dritten ist es untersagt, ohne Zustimmung des Inhabers der Marke im geschäftlichen Verkehr in Bezug auf Waren oder Dienstleistungen
ein mit der Marke identisches Zeichen für Waren oder Dienstleistungen zu benutzen, die mit denjenigen identisch sind, für die sie Schutz genießt,
Third parties shall be prohibited, without the consent of the proprietor of the trade mark, from using in the course of trade in relation to goods or services
Use a sign identical with the trademark for goods or services identical with those for which it enjoys protection,
So the name is in no way "safe".
Given that there is "YouTrack", "uTrack" and even "u-track" already, don't you want a unique brand people can recognize as yours? Isn't that the point of a name?