I don't know of anything like this in US practice, hence have no EN name for it. Suggest seated, appointed, or designated.) The popular judge seems to be chosen like a juror but is seated on the bench like a judge, alone except for one or two regular (robed) judges. In US, presiding judge can be a permanent position like chief judge/justice, or sometimes that title may be applied to any judge in charge of a particular hearing with other accompanying judges. In the latter case (unless the jurisdiction describes all supporting judges at a given hearing as presiding or associate) any supporting judges could be simply judges. At least that has been my experience although it could be a local custom.

By that logic, I would call the popular judge the presiding popular judge, or more likely a seated popular judge to prevent any inference that they are permanently the chief or presiding judge.

See criticized Wiki link below.

compare a Schoeffengericht in DE. Sits and deliberates with the Presiding Judge.

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Note added at 1 day 12 hrs (2020-02-24 11:16:33 GMT)
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PS: the active, 'effective' or effectual part played in the adjudication contrasts with an *observer-only* lay judge - as in the German legal system where the judge is flanked by up to two lay 'judges' who play no part in the ruling handed down, but consult in the deliberations with the judge retiring during an adjournment, mainly in criminal trials.