Slovak is what Slovakia reads
Slovakia works in Slovak, so Slovak is what your paper becomes. A certified translation into Slovak in Sheffield is written from a scan, and your English document never leaves your hands. The finished pages arrive signed and dated by a translator appointed by a court, which is the standing Slovak offices look for on a text of this kind.
Grammar that moves the ending
Slovak nouns change shape depending on what they are doing in a sentence. Say that a paper belongs to someone, or that it was issued to them, and the ending of their name moves with the meaning. Native writers do it without thinking, and to a Slovak eye a name left rigid can look slightly odd on the page.
On a record it has to look slightly odd. The version that matters is the one printed on your English certificate, letter for letter, because that is what a clerk holds up against everything else in your file. So the sentence gives way instead. A short linking word does the grammatical work, and the name sits inside it unchanged.
One spelling across the whole file
The trouble a name causes is never in one document. It shows up when two or three are read together and the same person appears in two or three shapes. A middle name present on one paper and missing from another, a hyphen that survives in one place, an accent dropped somewhere along the way: each looks trivial alone and suspicious in a stack.
So the useful thing you can do costs a minute. Before the writing starts, say which spelling already appears on any Slovak paperwork you hold, and whether it differs from your English certificate. A known difference can be stated openly in the finished set. A difference nobody mentioned turns into a question from Bratislava long after you have stopped thinking about it.
Cost and timing
The rate is £25 a page and the count is settled from your scans up front, so nothing about the bill moves later. Standard work takes 2–4 business days from a legible scan and the express route finishes in 24–48 hours. Both give you the same signed set, and the care taken over names is identical on either route.