His forename is known from Foster's Alumni Oxonienses for his son John, as is his residence.
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Their children found in christenings in Rochford, Worcestershire:

Name            Events            Location            Father          Mother
Thos.  Morris  29 December 1756  ROCHFORD,WORCESTER  Michael Morris  Margaret
Philip Morris  22 October  1759  ROCHFORD,WORCESTER  Michael Morris  Margaret
Margr. Morres  14 February 1762  ROCHFORD,WORCESTER  Michl. Morres   Margt.
John   Morris  25 January  1765  ROCHFORD,WORCESTER  Michael Morris  Margaret

No sign of a Michael who was named as the uncle of Elliot Morres in a monument put up by him in Tenbury church in 1835.

I do not think that their name was Morres.  If anything it was adopted after marriage and then possibly by error on the part of the record-keeper.
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This is a possibility for his burial, being the only such in Rochford within the period of 1761 to 1831.

First name(s)   Michael
Last name       Morris
Birth year      -
Death year      1784
Burial year     1784
Burial date     27 Aug 1784
Church          St Michael
Denomination    Anglican
Place           Rochford
County          Worcestershire
Country         England
Record set      National Burial Index For England & Wales
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No marriage record found from 1747 to 1767 anywhere in England on FindMyPast