Usually Willsons have the model number engraved on the mouthpiece receiver (not sure if that's the case with the older ones, which this particular one seems to be).
If in doubt, you could email Willson directly at info@Willson.ch with the serial number and they should be able to tell you. I emailed them awhile back and Mr. Kurath was quite prompt with responding, so it's worth a shot!
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)