Insofar as you feel like digging through further Japanese pages, here's (as far as I can tell) the right non-romaji search term: 心の風邪

(Edit for clarification: 心 is kokoro (soul), の is no (possessive marker), 風邪 is kaze (cold). As far as I can tell, the hospital's name only contains the substring 心の風, not the full thing; while that still can have the same literal meaning (風 as a standalone word is still read as 'kaze' and still can, among other meanings, mean cold), as far as I can tell from a bit of searching, it lacks the idiomatic 'depression' meaning that 心の風邪 has.