You can activate Thrun's last ability in response to Day of Judgment to create a regeneration effect on Thrun (C.R. 701.15a, 701.15c, 117.7); if that ability resolves, there will generally be two replacement effects that would replace Thrun being destroyed with something else: regeneration and totem armor (C.R. 701.15a, 702.88a, 303.4k).
When Day of Judgment resolves, all creatures would be destroyed. However, in the case of Thrun in this scenario, you choose which effect applies instead to Thrun if it would be destroyed — totem armor or regeneration (C.R. 616.1) — and you either remove all damage marked on Thrun and destroy Spider Umbra (C.R. 702.88a, 303.4k), or remove all damage marked on Thrun, tap it, and remove it from combat (C.R. 701.15a).
If Day of Judgment were replaced with Wrath of God, the situation would be different — regeneration effects won't keep creatures from being destroyed by Wrath of God (C.R. 701.15c; see also C.R. 608.2c, 101.2). Because Thrun's regeneration effect won't work here, the only remaining effect replacing Thrun being destroyed is totem armor, so that instead of Thrun being destroyed, you remove all damage marked on Thrun and destroy Spider Umbra (C.R. 702.88a, 303.4k) (and Thrun's regeneration effect will remain until end of turn [C.R. 701.15a]).
EDIT (Feb. 4): Add rule citations.
EDIT (Mar. 25): Correctness edit.
EDIT (Mar. 13, 2021): Some rules were renumbered in the meantime.
Thank you. Another question: if i regenerate in response to a DoJ, and that resolves, and they cast a second DoJ, do I have to regenerate a second time?
Thank you. Another question: if i regenerate in response to a DoJ, and that resolves, and they cast a second DoJ, do I have to regenerate a second time?
In the scenario in comment 1—
if totem armor kept Thrun from being destroyed from the first Day of Judgment, rather than regeneration, Thrun will continue to have the regeneration effect until end of turn (C.R. 701.15a), so that it's generally not necessary to give it another regeneration effect.
if regeneration kept Thrun from being destroyed from the first Day of Judgment, Thrun's regeneration effect will not apply to future events that would destroy Thrun (under C.R. 701.15a, regeneration from an activated ability applies only to the "next time [the permanent in question] would be destroyed this turn"); you will need to create another regeneration effect on Thrun (e.g, by activating Thrun's last ability again and having it resolve) (C.R. 701.15a), rely on totem armor (C.R. 702.88a, 303.4k), or have some other way to keep Thrun from being destroyed if you don't want Thrun to be destroyed.
EDIT (Feb. 4): Add rule citation.
EDIT (Mar. 13, 2021): One rule was renumbered in the meantime.
Thrun the Last Troll
Day of Judgement
If I have Thrun onboard and enchanted with Spider Umbra, if some one plays DoJ can I regenerate to keep the umbra from being destroyed?
When Day of Judgment resolves, all creatures would be destroyed. However, in the case of Thrun in this scenario, you choose which effect applies instead to Thrun if it would be destroyed — totem armor or regeneration (C.R. 616.1) — and you either remove all damage marked on Thrun and destroy Spider Umbra (C.R. 702.88a, 303.4k), or remove all damage marked on Thrun, tap it, and remove it from combat (C.R. 701.15a).
If Day of Judgment were replaced with Wrath of God, the situation would be different — regeneration effects won't keep creatures from being destroyed by Wrath of God (C.R. 701.15c; see also C.R. 608.2c, 101.2). Because Thrun's regeneration effect won't work here, the only remaining effect replacing Thrun being destroyed is totem armor, so that instead of Thrun being destroyed, you remove all damage marked on Thrun and destroy Spider Umbra (C.R. 702.88a, 303.4k) (and Thrun's regeneration effect will remain until end of turn [C.R. 701.15a]).
EDIT (Feb. 4): Add rule citations.
EDIT (Mar. 25): Correctness edit.
EDIT (Mar. 13, 2021): Some rules were renumbered in the meantime.
EDIT (Mar. 13, 2021): One rule was renumbered in the meantime.