Code to make TeXForm general special function names in full

Thanks to CallWolf code from https://mathematica.stackexchange.com/questions/153876/is-it-possible-to-change-customize-some-conversions-done-by-texform

SetOptions[EvaluationNotebook[],CodeAssistOptions->{"FloatingElementEnable"->False}]

Carl code. Evaluate this first

Initial/:Verbatim[TagSetDelayed][Initial[sym_],lhs_,rhs_]:=With[{new=Block[{sym},TagSetDelayed[sym,lhs,rhs];
First@Language`ExtendedDefinition[sym,"ExcludedContexts"->{}]],protect=Unprotect[sym]},sym;
Replace[new,Rule[values_,n:Except[{}]]:>(values[sym]=Prepend[values[sym],n]),{2}];
Protect@protect;]

(*DO NOT USE THIS. Causes a bug. see https://mathematica.stackexchange.com/questions/270972/bad-latex-generated-when-using-texform-with-another-answer-solution *)
(*System`Convert`TeXFormDump`maketex[s_String]/;!StringMatchQ[s,"\""~~___~~"\""]&&SyntaxQ[s,TeXForm]:=Replace[s,{n_/;StringMatchQ[n,NumberString]:>n,w_?wordQ:>"\\operatorname{"<>w<>"}"}]&*)

wordQ[s_String]:=Length@StringSplit[s,WordBoundary]==1

Initial[Convert`TeX`ExpressionToTeX]/:Convert`TeX`ExpressionToTeX[e__]/;!TrueQ@$TeX:=Block[{$TeX=True},Convert`TeX`ExpressionToTeX[e]]

Now adding my own code for any special function need to be changed.

Initial[FresnelC]/:MakeBoxes[FresnelC[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[FresnelC][a],TraditionalForm];
Initial[CosIntegral]/:MakeBoxes[CosIntegral[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[CosIntegral][a],TraditionalForm];
Initial[AiryAiPrime]/:MakeBoxes[AiryAiPrime[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[AiryAiPrime][a],TraditionalForm];
Initial[AiryAi]/:MakeBoxes[AiryAi[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[AiryAi][a],TraditionalForm];
Initial[BesselI]/:MakeBoxes[BesselI[a_,n_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[BesselI][a,n],TraditionalForm];

Initial[BesselJZero]/:MakeBoxes[BesselJZero[a_,n_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[BesselJZero][a,n],TraditionalForm];
Initial[BesselJZero]/:MakeBoxes[BesselJZero[a_,n_,x0_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[BesselJZero][a,n,x0],TraditionalForm];

Initial[BesselJ]/:MakeBoxes[BesselJ[a_,n_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[BesselJ][a,n],TraditionalForm];

Initial[Erfi]/:MakeBoxes[Erfi[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Erfi][a],TraditionalForm];
Initial[ExpIntegralEi]/:MakeBoxes[ExpIntegralEi[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ExpIntegralEi][a],TraditionalForm];
Initial[HypergeometricU]/:MakeBoxes[HypergeometricU[a_,b_,c_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[HypergeometricU][a,b,c],TraditionalForm];
Initial[LaguerreL]/:MakeBoxes[LaguerreL[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[LaguerreL][a,b],TraditionalForm];
Initial[LaguerreL]/:MakeBoxes[LaguerreL[a_,b_,x_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[LaguerreL][a,b,x],TraditionalForm];

Initial[HermiteH]/:MakeBoxes[HermiteH[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[HermiteH][a,b],TraditionalForm];

Initial[Hypergeometric1F1]/:MakeBoxes[Hypergeometric1F1[a_,b_,c_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Hypergeometric1F1][a,b,c],TraditionalForm];

Initial[Hypergeometric2F1]/:MakeBoxes[Hypergeometric2F1[a_,b_,c_,d_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Hypergeometric2F1][a,b,c,d],TraditionalForm];
Initial[HypergeometricPFQ]/:MakeBoxes[HypergeometricPFQ[a_,b_,c_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[HypergeometricPFQ][a,b,c],TraditionalForm];

HypergeometricU;
Initial[HypergeometricU]/:MakeBoxes[HypergeometricU[a_,b_,z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[HypergeometricU][a,b,z],TraditionalForm];

Initial[Erfc]/:MakeBoxes[Erfc[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Erfc][a],TraditionalForm];
Initial[Erf]/:MakeBoxes[Erf[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Erf][a],TraditionalForm];
Initial[Erf]/:MakeBoxes[Erf[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Erf][a,b],TraditionalForm];

Initial[ExpIntegralE]/:MakeBoxes[ExpIntegralE[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ExpIntegralE][a,b],TraditionalForm];

ParabolicCylinderD;
Initial[ParabolicCylinderD]/:MakeBoxes[ParabolicCylinderD[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ParabolicCylinderD][a,b],TraditionalForm];
Initial[ProductLog]/:MakeBoxes[ProductLog[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ProductLog][a],TraditionalForm];
Initial[ProductLog]/:MakeBoxes[ProductLog[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ProductLog][a,b],TraditionalForm];

DawsonF;
Initial[DawsonF]/:MakeBoxes[DawsonF[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[DawsonF][a],TraditionalForm];
Initial[EllipticF]/:MakeBoxes[EllipticF[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[EllipticF][a,b],TraditionalForm];

Initial[Gamma]/:MakeBoxes[Gamma[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Gamma][a],TraditionalForm];
Initial[Gamma]/:MakeBoxes[Gamma[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Gamma][a,b],TraditionalForm];
Initial[Gamma]/:MakeBoxes[Gamma[a_,b_,c_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[Gamma][a,b,c],TraditionalForm];

Initial[LogIntegral]/:MakeBoxes[LogIntegral[a_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[LogIntegral][a],TraditionalForm];

Initial[PolyLog]/:MakeBoxes[PolyLog[a_,b_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[PolyLog][a,b],TraditionalForm];
Initial[PolyLog]/:MakeBoxes[PolyLog[a_,b_,c_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[PolyLog][a,b,c],TraditionalForm];

ProductLog;
Initial[ProductLog]/:MakeBoxes[ProductLog[z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ProductLog][z],TraditionalForm];
Initial[ProductLog]/:MakeBoxes[ProductLog[k_,z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ProductLog][k,z],TraditionalForm];

ArcCos;
Initial[ArcCos]/:MakeBoxes[ArcCos[z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ArcCos][z],TraditionalForm];
ArcSin;
Initial[ArcSin]/:MakeBoxes[ArcSin[z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ArcSin][z],TraditionalForm];
ArcTan;
Initial[ArcTan]/:MakeBoxes[ArcTan[z_],TraditionalForm]/;$TeX:=MakeBoxes[Defer[ArcTan][z],TraditionalForm];