Change the word "Table" in table captions

Since you are using babel with the spanish option, the default behaviour is to use "Cuadro" as \tablename (following a recommendation from the RAE); however, it is also usual, and many people prefer this regardless of what the RAE says) to use "Tabla" instead. You can use the es-tabla option for babel to change the name to "Tabla":

\usepackage[spanish,es-tabla]{babel}

Another option to get "Tabla" is to use the mexico package option

\usepackage[spanish,mexico]{babel}

but this option also changes the behaviour of the quotation marks and of the decimal separator (for details, texdoc spanish on a terminal).

If you want to change the name to some other string, you can redefine \spanishtablename:

\usepackage[spanish]{babel}
\renewcommand\spanishtablename{Otro nombre}

You can use the caption package like in the following

\documentclass[12pt, letterpaper]{article}
\usepackage{caption}
\captionsetup[table]{name=New Table Name}

\begin{document}

\begin{table}\centering
\begin{tabular}{|c|c|}
test & test\\
\end{tabular}
\caption{test caption}
\end{table}

\end{document}

With KOMA-Script

If you use package babel together with KOMA-Script (to be correct, package scrbase, which is called in the KOMA-Script classes scrartcl, scrreprt, scrbook and scrlttr2 and in the KOMA-Script package scrextend) it is better to use the mechanism of KOMA-Script instead of babels because KOMA-Script has a better verification.

KOMA-Script defines two macros for naming or renaming LaTeX names:

\newcaptionname{language}{LaTeX name}{new content}   % new name
\renewcaptionname{language}{LaTeX name}{new content} % renew existing name

For your case it is enough to add:

\renewcaptionname{spanish}{\listtablename}{Índice de tablas}
\renewcaptionname{spanish}{\tablename}{Tabla}

Please note that with loading the package scrextend (see chapter 16, file scrguien.pdf, texdoc scrguien) you can use some KOMA-Script features with non KOMA-Script classes. For example scrextend loads scrbase.