documentclass[a4paper]{article}

usepackage{hyperref}
usepackage{glossaries}

makeglossaries
newglossaryentry{lowercase}{name={lowercase}, description={In the glossary, this word should be capitalized}}
newglossaryentry{uppercase}{name={Uppercase}, description={This word is capitalized}}

begin{document}

Should both be lowercase: gls{lowercase}, gls{uppercase}.

Workaround: gls{lowercase}, glslink{uppercase}{uppercase}.

printglossaries

end{document}

Should both be lowercase: lowercase, Uppercase.
Workaround: lowercase, uppercase.

Glossary
lowercase In the glossary, this word should be capitalized. 1
Uppercase This word is capitalized. 1

newglossaryentry{uppercase}{
    name={Uppercase},
    text={uppercase},
    description={Appears uppercase in the glossary and lowercase in the text}
}

usepackage{mfirstuc}
renewcommand{glsnamefont}[2][]{capitalisewords{#1}xspace#2}

newglossaryentry{firstexample}{
  name={first}{word capitalized}
}

newglossaryentry{boite}{
  name={Boite de valeurs},
  text={boite de valeurs}
}

newglossaryentry{iblabla}{
  name={$i$-th blabla}
}

setglossarystyle{long}
setabbreviationstyle[acronym]{long-short}
glssetcategoryattribute{acronym}{glossdesc}{firstuc}

newglossaryentry{concept}{
name={Concept},
text={concept},
description={definition of concept},
plural={concepts}
}