First of, I understand and respect that the point of this subreddit is not to help people with their homework, but I have hit a dead end in researching this and would immensely appreciate any suggestions or pointers to literature.
The book in question is "Thomas Wright, The disposition or garnishmente of the soule to receive worthily the blessed sacrament. Antwerpe 1596"
The book states that it was printed in Antwerp by Joachim Trognaesius. However, some secondary sources suggest that it was in fact printed by the English secret press in England, and that the printer's name was added as a cover. The book does not contain an imprimatur, nor does it seem to have been granted a privilege. As far as I can tell, it was printed in secret by Catholics in England under Elisabeth the first. It is a theological book, dealing with various practices of the catholic Eucharist.
I do not know of any majorly important figures whose initials fit, nor can I seem to find anything by just googling the initials, as doing so only refers me to a handful of books that either contain a transcription of the full dedication, or that state that they are as of yet unidentified. http://oaktrust.library.tamu.edu/bitstream/handle/1969.1/ETD-TAMU-1111/GARCIA-DISSERTATION.pdf --> ctrl+f mistris
I tried researching the author, Thomas Wright, and found some interesting information but no names to fit these initials. https://en.wikipedia.org/wiki/Thomas_Wright_(controversialist)
Thank you kindly in advance, I fully understand that this is a niche question.
On the specific question of trying to find out who the dedicatees were, that would be a great deal of work in itself. The key word here is "recusants" - which officially meant those who refused to attend Anglican mass, but is commonly used to mean people who remained Catholic after England had become Protestant. There were a number of gentry and otherwise prominent families who did.
It's possible that an academic or PhD student who has been immersed in recusancy literature and records might recognise the initials. But it's also possible the records don't exist to tie these people in with recusancy - and even if they do, it may be a considerable slog to find them. And some people were Catholic whilst also attending Anglican services.
Recusancy became an offence in 1581, and court records are a source of names on that basis. Many recusancy records are not digitised and some are not centralised. As this search result shows, you need to visit the National Archives to look through the document (a recusancy roll). Some records will be in local archives instead of in London.
In less reliable sources, there is a long list of "recusant families" which appears on Wikipedia and global genealogy site Geni. The source of this is unclear. The Wikipedia page links some of the names to a genealogy blog. The Geni list does not link to any records on the site. The surnames beginning with H could be used as a starting point, but without primary sources, the research wouldn't be suitable for an academic paper, and would be more of a personal hobbyist timesink.
As the old recusancy records are not digitised, the names couldn't be used for this anyway, but someone could have a go with them on genealogy sites. (It would be a questionable use of time for someone who may have other priorities, such as a postgrad student, and even more so if there wasn't the possibility of easily cross-checking primary records - I am guessing that you may not be in the UK and if so, travel to the archives only for this would be prohibitively expensive.)
Geni and its sister site MyHeritage (both feature the same genealogical data added by users) can be partially searched without subscription. (For example here is a record for Anne Howard nee Dacre - names of other people can be clicked on if you can get into one record like that via a google search. But they are easier to search with subscription. There are also some other genealogy sites where trees are displayed publicly and can be found through web search. Using the name list, in combination with other info available about some of the families, it may be possible to track down some genealogies and see what the names were of people alive at the time Wright wrote. (And of course this wouldn't be academic standard without cross-checking against other sources for the people's Catholicism and existence.) But the info may not be available: the trees might be private, never have been put online, any records about these individuals may have been lost. Or the lines may have died out, so no-one has cared to put the info in a genealogy.
Basically, you would be looking at a lot of time and expense for something that it's uncertain still exists to be found.
Digging up all available biographical info on Wright, such as the areas of England where he spent time, and who he associated with - and considering Catholic families in those areas and social circles, is another possible route, but again far from certain.