It's not entirely clear if you're saying you want the descriptor of the table to show up in the TOC or the entire table!

First things first. Make sure all of your TOC styles are updated as you want them to show up in the TOC. A style in the body of the document is different than what shows up in the TOC style.

For the descriptor to show up, i.e., Table 1 and Tables 2, place the table name text in a heading like you've already done. Heading Table Title.

Now go to References >> Table of Contents >> Custom Table of Contents

Select the Table of Contents tab >> Options >> Place a TOC reference against the TOC level

i.e.,
Heading 1 >> 1
Heading 2 >> 2
Table Title >> 3

When you back out of this option, Word will prompt you for updating the TOC.