By changing the STRINGS.txt files within the TEXT folder, you can name the weapons whatever you wish.
In this case, I've gone for weapon names relating to the models the games weapons are based on to the best of my knowledge.
For weapons such as the rocket and grenade launcher, no such real world equivalent exists, as far as I know. I've either left these alone. I've also made slight changes to the way ammo is named.
Names changed for TR1:
Pistols: Dual Browning HPs
Shotgun: Mossberg 500
Magnum: Dual Desert Eagles
Uzis: Dual MAC-10s
Names changed for TR2:
Pistols: Dual Browning HPs
AUTOS=Dual TEC-22s (Thank you, CyborgParrot)
Shotgun: Mossberg 500
Magnum: Dual Desert Eagles
Uzis: Dual MAC-10s
Automatic Pistols: Dual Auto Pistols
M16: M16
Names changed for TR3:
Pistols: Dual Browning HPs
Shotgun: Mossberg 500
Magnum/Deagle: Desert Eagle
Uzis: Dual MAC-10s
MP5: HK MP5
You can edit the files yourself with a simple text editing program, or you can download these as is from here.
Names also changed for Ammo across all 3 games:
PISTOLAMMO=Pistol Ammunition
SHOTGUNAMMO=12 Gauge Shells
MAGNUMAMMO=Magnum Ammunition
AUTOSAMMO=5.6×15mmR Ammunition
UZIAMMO=MAC-10 Ammunition