How can I change the color of a multirow-column when I defined the color of each row?

Here is a way, with clines and cellcolor. Note it is not a good idea to denote a new column type as w; this specifier is defined in recent versions of the array package.

    documentclass{article}
    usepackage{array}
    usepackage{multirow}
    usepackage[table]{xcolor}
    definecolor{NbaBlue}{RGB}{181, 191, 245}
    definecolor{NbaRed}{RGB}{245, 187, 181}

    begin{document}

    begin{table}[!h]
    begin{tabular}{c !{{color{white}vrule}}!{color{white}vrule} l !{color{white}vrule} l}
    rowcolor{NbaRed} 1. & Philadelphia 76ers &  cellcolor{white} 
    cline{1-2}
    rowcolor{NbaBlue} 2. & Brooklyn Nets 
    cline{1-2}
    rowcolor{NbaRed} 3. & Milwaukee Bucks 
    cline{1-2}
    rowcolor{NbaBlue} 4. & Atlanta Hawks 
    cline{1-2}
   rowcolor{NbaRed} 5. & Miami Heat 
    cline{1-2}
    rowcolor{NbaBlue} 6. & New York Knicks 
    cline{1-2}
    rowcolor{NbaRed} 7. & Boston Celtics 
    cline{1-2}
     rowcolor{NbaBlue}8. & Charlotte Hornets & multirow{-8}{6cm}{cellcolor{white}Die NBA ist in zwei Konferenzen (engl. Conferences) eingeteilt. Die Eastern und die Western Conference. Beide bestehen aus 15 verschiedenen Teams. Diese Tabelle zeigt die momentan 8 besten Teams der Eastern Conference.} 
    %hline
    end{tabular}
    caption{Eastern Conference}
    label{}
    end{table}

end{document} 

What about something like the following?

documentclass{article}
usepackage{array}
usepackage{multirow}
usepackage[table]{xcolor}
definecolor{NbaBlue}{RGB}{181, 191, 245}
definecolor{NbaRed}{RGB}{245, 187, 181}

begin{document}

begin{table}[!h]
centering
  rowcolors{1}{NbaRed}{NbaBlue}
  begin{tabular}{c !{{color{white}vrule}}!{color{white}vrule} l !{color{white}vrule}}
    1. & Philadelphia 76ers   hline
    2. & Brooklyn Nets        hline
    3. & Milwaukee Bucks      hline
    4. & Atlanta Hawks        hline
    5. & Miami Heat           hline
    6. & New York Knicks      hline
    7. & Boston Celtics       hline
    8. & Charlotte Hornets    hline
  end{tabular}
  quad
  begin{minipage}{0.5textwidth}
  raggedright
    Die NBA ist in zwei Konferenzen (engl. Conferences) eingeteilt. Die Eastern und die Western Conference. Beide bestehen aus 15 verschiedenen Teams. Diese Tabelle zeigt die momentan 8 besten Teams der Eastern Conference.
  end{minipage}
  caption{Eastern Conference}
  label{}
end{table}

end{document} 

With {NiceTabular} of nicematrix.

documentclass{article}
usepackage{xcolor}
usepackage{caption}
usepackage{nicematrix,tikz}

begin{document}

begin{table}[h]
    centering
    begin{NiceTabular}{>{arabic{iRow}.}clp{6cm}}
    CodeBefore
    rowcolors[RGB]{1}{245, 187, 181}{181, 191, 245}[cols={1,2}]
    tikz draw [white,very thick] (1-|2) -- (last-|2) ;
    Body
    cline{1-2}
    & Philadelphia 76ers & Block{*-1}{parbox{6cm}{Die NBA ist in zwei Konferenzen (engl. Conferences)
        eingeteilt. Die Eastern und die Western Conference. Beide bestehen aus 15 verschiedenen Teams. Diese
        Tabelle zeigt die momentan 8 besten Teams der Eastern Conference.}}  cline{1-2}
    & Brooklyn Nets   cline{1-2}
    & Milwaukee Bucks  cline{1-2}
    & Atlanta Hawks  cline{1-2}
    & Miami Heat  cline{1-2}
    & New York Knicks   cline{1-2}
    & Boston Celtics  cline{1-2}
    & Charlotte Hornets  cline{1-2}
    end{NiceTabular}
    caption{Eastern Conference}
    label{}
end{table}

end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).