I need a script that could take in a line from one file and match the line up with codes in the order file.

My first file, called names.txt ,contains:
>123456789
>987654321
>15946873
>157987513

The other file, called data,contains:
GB_00012.faa
GB_6789333.faa
GB_100098.faa
GB_1237700.faa

All the data files contain a line startin with ">" symbol, and contain after that point somwhere the names.txt identifier. Ideally I would love the output to be:
>123456789 GB_1237700.faa >line from GB file.

I know how to do it manually using grep, but having around 10000 different identifiers and three coupled files together, would take me ages to go through one by one. If this is possible to make in a script, I'd be really thankful for the help!

Something like this may get you started:

#!/bin/bash
declare -a data_files=()
while IFS= read -r file; do data_files+=("$file"); done < "data"
while IFS='>' read -r _ code; do
        grep -H "$code" "${data_files[@]}"
done < "names.txt"