I didn't Latinize the names, but if you want to do that, I'd expect Anneka or Anna for the Queen's name and Mathildam or Matildam for yours (your name goes in the accusative). "Consociam" makes you a feminine companion; if you want to be a masculine (and therefore gender-unspecified) companion, use "consocium". I didn't find a perfect Latin translation for "induct"; Cassell's gives "inauguro", but that seems to have had heavy religious overtones (think "augury") as well as being the root of "inaugurate". I used "creo", which can mean either "make" or "elect" as in "elect to office". The French order texts I've looked at often use a word that translates as "elect", which reflects the fact that members of period orders were often nominated by a voting process (of course, smart companions voted for the person the Sovereign wanted!)
I looked at the period Latin grant of arms texts here for some vocabulary:
no subject
Nos, Ragnarr Rex et Anneke Regina, creamus Mathilde Bourré consociam Ordinis Nostri Lauri XXIV Die Martii Anno Societatis XLI. Et, per litteras nostras patentes, damus et concedimus haec arma.
We, King Ragnarr and Anneke Regina, make Mathilde Bourré a companion of Our Order of the Laurel on the 24 Day of March A.S. 41. And, by our letters patent, we give and hand over these arms.
I didn't Latinize the names, but if you want to do that, I'd expect Anneka or Anna for the Queen's name and Mathildam or Matildam for yours (your name goes in the accusative). "Consociam" makes you a feminine companion; if you want to be a masculine (and therefore gender-unspecified) companion, use "consocium". I didn't find a perfect Latin translation for "induct"; Cassell's gives "inauguro", but that seems to have had heavy religious overtones (think "augury") as well as being the root of "inaugurate". I used "creo", which can mean either "make" or "elect" as in "elect to office". The French order texts I've looked at often use a word that translates as "elect", which reflects the fact that members of period orders were often nominated by a voting process (of course, smart companions voted for the person the Sovereign wanted!)
I looked at the period Latin grant of arms texts here for some vocabulary:
http://verysleepy.itgo.com/grants.htm
http://verysleepy.itgo.com/private.htm
If you want a longer & fancier scroll text, I can give you some suggestions based on these examples without doing a whole lot more work.