Maybe emotionally, it might be important to your wife. But for (most of) the US government, it's not and it could be illegal if you sign the wrong paperwork, like what happened in the case referenced above by @Verrou. As others mentioned, if you were already legally married in the Philippines, then the US also recognizes your marriage as legal.
If having a US-issued certificate is what your wife wants, then look into vow renewals (as @Loren Y suggested) or foreign marriage registration. Other than Nevada, New Jersey and Colorado issue official certificates for such cases. Colorado, in particular, allows "re-marriage" as the Colorado DMV does not accept foreign marriage certificates as legal name change documents! Check the links below for more info --
New Jersey ("reaffirm your relationship/vows by registering a remarriage") -- https://www.nj.gov/health/vital/registration-vital/marriage-licenses/#6
Colorado -- https://www.visajourney.com/forums/topic/761702-changing-last-name-after-immigration-of-spouse/?do=findComment&comment=10580622