Please use the Question Tags to state the name and full version number of the Story Format (and/or the Twine Compiler) you are using, instead of including that information within your question.
You can use the (datanames: ) macro to obtain the name of each item contained within your $Inv data-map, and then use the (find:) macro to create an array containing the names of the items that currently equal true.
(set: $Inv to (datamap: "pet", false, "box", true, "figure", false, "necklace", true, "wrench", false))
(set: _have to (find: _item where ($Inv's (_item)), ...(datanames: $Inv)))
You are Carring: _have
If you want the output of the above _have variable to look slightly better then you could also use the Java-script <Array>.join() function to generate the coma separated list like so.
You are Carring: (print: _have.join(", "))