Chronology
1846 formed as Regiment of Ludhiana
1861 became 15th Bengal Native Infantry
1864 became 15th (Ludhiana) Regiment of Bengal Native Infantry
1885 became 15th Regiment of Bengal Native Infantry (Ludhiana Sikhs)
1901 became 15th (Ludhiana) Sikh Infantry
1903 became 15th Ludhiana Sikhs
1922 became 2nd Bn/11th Sikh Regiment
1947 allocated to India on Partition
Corresponding items on Sikh website
1846-1864 15th Loodianah Regiment belt buckle/clasp.
1885-1922 15th Loodianah Sikhs Officers Pagri Badge (silver)
Interestingly ww1cemetaries shows headstones featuring both spellings and different badges.
https://www.ww1cemeteries.com/r-b-indian-regiments.html