How do I look up the unit names of prior duty stations?

2d LAI Bn, 2d MarDiv was your unit. During your time in the service your unit was located aboard Marine Corps Base (MCB) Camp LeJeune. Your platoon number at recruit training will tell you which Battalion you were in, i.e. I was in platoon 2095, therefore, I was in the 2d Battalion, Recruit Training Regiment (unit) aboard Marine Corps Recruit Depot Parris Island (location). If you went through Parris Island, after you completed boot camp, you were transferred to the School of Infantry - E(ast) (unit) at Camp Geiger (base or location) where you stayed either 29 days for Marine Combat Training if your MOS was not 03XX, or the Infantry Training Battalion (59 days) if you were an 03XX. After Camp Geiger, you were detailed to your MOS specific school, many of which are at Camp LeJeune, but many are elsewhere. you then would have been transferred back to 2d LAI.

So you are trying to determine your previous units you were assigned to? Look at your old orders. I don't know if the Marines have a similar document to the Army Enlisted Record Brief ERB / Soldier Record Brief SRB. It lists all your assignments in chronological order. That would be in a soldier's OMPF that you can request a copy of from NPRC.

Your records may be available through the VA eBenefits Dashboard. There is a link on that site. Try there.

https://www.hqmc.marines.mil/Agencies/Office-of-Legislative-Affairs/Congressional-Correspondence-Section/Records-Request/

This MPO contains details of what is in your field record. https://www.marines.mil/Portals/1/Publications/MCO%20P1070.12K%20W%20CH%201.pdf

The photo is of the page you may want to look at.