The closest I can get to "konkurzné konanie" in English is "job (or employee) selection procedure" - that is, unless you accept the expression "job interview", which focuses on the most important part of the selection procedure. There is an English word "concourse", but naturally its meaning is different from the Slovak "konkurz".

The old Latin idea of "running together" (which is preserved in Slovak together with the idea of competition, like who will "win" the job - or their investment back in cases of bankruptcy, when a company is "v konkurze") is changed into the idea of a meeting of people, a lot of people in a crowd, then the place where a crowd could meet, like a "korzo", a wide street or square, or the large hall inside a railway station or airport.

There is another kind of "konkurz", which is the selection procedure to find the best supplier to gain a contract from the customer or contractor. This should NOT be translated as "tender", because that means the "ponuka" submitted by the companies wanting the contract.