Here we call upon the name of the Lord. We ask for blessing, seek forgiveness, and intercede for our brothers and sisters. In the assembly prayers are not personal. The individual that leads in prayer is bringing the congregation before the throne of all grace.
Collective interests are to be the primary ones.
If individual concerns are made known, they should the kind that require collective faith and prayer. Prayers are addressed to God, but they are also for the benefit of the people. If they cannot be heard by the audience, they should not be uttered in their behalf. I have been in some assemblies where it was not possible to discern when certain prayers commenced, or when they ended. This is something that is not to be tolerated.