I don’t think technically a motion can be proposed without the proposer being identified and, unless the strata manager is an owner, they shouldn’t be proposing motions. (see extract form Schedule 1, Part 2, 4 below).
However, there’s nothing wrong with the chair putting their name to a procedural motion that has been proposed by an interested party. On the other hand, the chair could rule the motion out of order if it doesn’t have an owner’s name on it.
(1) Any owner, or any person entitled to vote at a general meeting of an owners corporation, may require a motion to be included in the agenda of the next general meeting of the owners corporation.
(2) The requirement is to be made by written notice given to the secretary of the owners corporation that:
(a) sets out the required motion, and
(b) states the name of the person making the requirement, and
(c) includes an explanation of the motion of not more than 300 words in length.