In terms of saying "John Doe, Sally Stevens, etc. submitted matching gifts through using our service", right now that isn't feasible on our end. This is due to the way the matching gift process is set up. Donors use the information we provide to actually submit the match requests directly through each company's individual system / process.
Our matching gift plugin currently only has one field, a company name, for donors to use. At one point we tested a second field for either an email address or individual's name. When measuring usage we found that the additional field resulted in fewer individuals beginning their search and ultimately fewer matching gifts being submitted.
After many conversations with clients we ultimately chose to incorporate the functionality that maximizes the amount of money organizations raise from matching gifts over the reporting / tracking of specific donors who use the tool so we removed that additional field from our search tool.