Norman Alling's Conway's field of surreal numbers (1985) gives full credit to Conway:

Conway introduced the field No of numbers, which Knuth has called the surreal numbers. No is a proper class and a real-closed field, with a very high level of density, which can be described by extending Hausdorff's $\eta_\xi$ condition. In this paper the author applies a century of research on ordered sets, groups, and fields to the study of No.

References to Alling's own 1962 paper appear only in passing, on page 373 and 377–378. The 1987 book referred to in the OP follows up on this 1985 exposition, which makes it clear that Alling in no way claims independence from Conway.

Norman Alling's Conway's field of surreal numbers (1985) gives full credit to Conway:

Conway introduced the Field No of numbers, which Knuth has called the surreal numbers. No is a proper class and a real-closed field, with a very high level of density, which can be described by extending Hausdorff's $\eta_\xi$ condition. In this paper the author applies a century of research on ordered sets, groups, and fields to the study of No.

References to Alling's own 1962 paper appear only in passing, on page 373 and 377–378. The 1987 book referred to in the OP follows up on this 1985 exposition, which makes it clear that Alling in no way claims independence from Conway.

Norman Alling's Conway's field of surreal numbers (1985) gives full credit to Conway:

Conway introduced the Field No of numbers, which Knuth has called the surreal numbers. No is a proper class and a real-closed field, with a very high level of density, which can be described by extending Hausdorff's $\eta_\xi$ condition. In this paper the author applies a century of research on ordered sets, groups, and fields to the study of No.

References to Alling's own 1962 paper appear only in passing, on page 373 and 377-378. The 1987 book referred to in the OP follows up on this 1985 exposition, which makes it clear that Alling in no way claims independence from Conway.

Norman Alling's Conway's field of surreal numbers (1985) gives full credit to Conway:

Conway introduced the field No of numbers, which Knuth has called the surreal numbers. No is a proper class and a real-closed field, with a very high level of density, which can be described by extending Hausdorff's $\eta_\xi$ condition. In this paper the author applies a century of research on ordered sets, groups, and fields to the study of No.

References to Alling's own 1962 paper appear only in passing, on page 373 and 377–378. The 1987 book referred to in the OP follows up on this 1985 exposition, which makes it clear that Alling in no way claims independence from Conway.