According to Bredow-Wedel, who is not always above doubt, but seems to be correct here, the subsequent names of the unit were:
On 12.2.1820 the 38. Infanterie-Regiment (6. Reserve-Regiment) was created.
On 18.9.1820 it was renamed 37. Infanterie-Regiment (5. Reserve-Regiment) (change of the army corps it was assigned to, the hitherto 37th regiment received the number 38 in exchange).
On 4.7.1860 it got the name Westphälisches Füsilier-Regiment (Nr. 37).
On 7.5.1861 this was slightly altered into Westphälisches Füsilier-Regiment Nr. 37
On 27.1.1889 it was renamed Füsilier-Regiment von Steinmetz (Westphälisches) Nr. 37.
As late as 27.1.1902 the provincial designation was changed into Füsilier-Regiment von Steinmetz (Westpreußisches) Nr. 37. This name was retained until the First World War.