What you want is to create a systemd unit file for your service. In that file, specify an After=mongod.service (the service file name can vary depending on your distribution).
Requires=multi-user.target will only ensure that your service is started after the multi-user runtime is reached. The order of services started is not deterministic, so it would be possible for your service to launch before mongod on one systemctl start myservice and after mongod the next time (depending on any other Unit configuration).
Requires=mongod.service is also not what you want:
Note that this dependency type does not imply that the other unit always has to be in active state when this unit is running. Specifically: failing condition checks (such as ConditionPathExists=, ConditionPathIsSymbolicLink=, … — see below) do not cause the start job of a unit with a Requires= dependency on it to fail. Also, some unit types may deactivate on their own (for example, a service process may decide to exit cleanly, or a device may be unplugged by the user), which is not propagated to units having a Requires= dependency. Use the BindsTo= dependency type together with After= to ensure that a unit may never be in active state without a specific other unit also in active state (see below).
https://www.freedesktop.org/software/systemd/man/latest/systemd.unit.html
WantedByof your script tomongod.service?