2

Consider this example:

\documentclass{report}
\usepackage{graphicx}
%% \usepackage[latvian]{babel}                                                                                                                                                                              
%% \addto\captionslatvian{\renewcommand{\figurename}{att.}}
%% the dot in "att." will replace ":" as the separator                                                                                                                                                 
\begin{document}
    \begin{figure}
      \includegraphics{example-image-a}
      \caption{Case of A.}
    \end{figure}
\end{document}

The output is

enter image description here

How can I remove the colon from the caption of the image?

The case is relevant for some languages that have other means of separation (see the commented out lines of code).

2

I suggest, since att. (with the dot) seems to be an abbreviation, which will be used in cross-references, to use labelsep=space:

\documentclass{report}

    \usepackage{graphicx}
     \usepackage[latvian]{babel}

\usepackage{caption}
\captionsetup[figure]{labelsep=space}
 \addto\captionslatvian{\renewcommand{\figurename}{att.}}
    %% the dot in "att." will replace ":" as the separator

    \begin{document}

    \begin{figure}
      \includegraphics{example-image-a}
      \caption{Case of A.}
    \end{figure}

\end{document} 

enter image description here

3

With the help of the caption package:

enter image description here

\documentclass{report}
    \usepackage{graphicx}
     \usepackage[latvian]{babel}                                                                                                                                                                              
     \addto\captionslatvian{\renewcommand{\figurename}{att}}
     \usepackage[labelsep=period]{caption}
    \begin{document}
    \begin{figure}
      \includegraphics{example-image-a}
      \caption{Case of A.}
    \end{figure}
\end{document}

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