I wouldn't be suspecting the oil pump unless it's been fed a steady diet of sand and engine shrapnel. As said above, they're gear pumps and last a very long time, typically the service life of the engine.

Make sure you're using the correct weight of engine oil. Original spec was 15W-40, if you're using 30 weight oil, you can expect the oil pressure to be low.

Normal hot idle oil pressure on the OM60x engines is ~1bar. Depending on the sensor and the electrical integrity of your vehicle, the gauge may not reflect that properly. Does the oil pressure build quickly when the engine is revved? You should have the gauge pegged by 2K RPM. If it does, the oil pump is fine.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]