Being or not being open source makes fairly little difference in trademark law.

If a commercial firm (Yoyodyne, say) had used the name "Portable Network Graphics" and the abbreviation "PNG" in trade, and taken such further steps as would be needed to protect it in the relevant countries, that firm would have a protectable trademark.

Note that is some countries, a trademark must be registered to have any protection at all (much of the EU follows this rule). In others, use in commerce can offer some protection even without registration (the US follows this rule).

Had this happened (in an alternate reality) Yoyodyne could have sent a cease and desist letter when open source developers started using the mark. If the devs did not cease, Yoyodyne might have obtained an injunction, or damages for trademark infringement, or both.

But had Yoyodyne failed to defend the mark effectively and allowed it to become generic, Yoyodyne might have lost all rights to it. Also, had Yoyodyne ceased to use it in trade for a significant period, they might have lost rights. This is a place where the different laws in different countries might lead to different results.

Note that "Portable Network Graphics" is rather descriptive, and not particularly distinctive. Descriptive marks, like "Tasty Pizza" generally get weaker protection, while more distinctive marks, such as "LuAnn's Tastee Pizza" are more strongly protected, in general. Again this depends on the country, and the specific facts.

In general the first to use, or to register a mark, gets the rights. When one entity is the first to use, but a different one is first to register, things can get confusing, and results will be different in different countries.

Being or not being open source makes fairly little difference in trademark law.

If a commercial firm (Yoyodyne, say) had used the name "Portable Network Graphics" and the abbreviation "PNG" in trade, and taken such further steps as would be needed to protect it in the relevant countries, that firm would have a protectable trademark.

Note that in some countries, a trademark must be registered to have any protection at all (much of the EU follows this rule). In others, use in commerce can offer some protection even without registration (the US follows this rule).

Had this happened (in an alternate reality) Yoyodyne could have sent a cease and desist letter when open source developers started using the mark. If the devs did not cease, Yoyodyne might have obtained an injunction, or damages for trademark infringement, or both. They could also have issued a takedown notie to the site hosting the project.

But had Yoyodyne failed to defend the mark effectively and allowed it to become generic, Yoyodyne might have lost all rights to it. Also, had Yoyodyne ceased to use it in trade for a significant period, they might have lost rights. This is a place where the different laws in different countries might lead to different results.

Note that "Portable Network Graphics" is rather descriptive, and not particularly distinctive. Descriptive marks, like "Tasty Pizza" generally get weaker protection, while more distinctive marks, such as "LuAnn's Tastee Pizza" are more strongly protected, in general. Again this depends on the country, and the specific facts.

In general the first to use, or to register a mark, gets the rights. When one entity is the first to use, but a different one is first to register, things can get confusing, and results will be different in different countries.

Note that a Cease and Desist letter is not a legal requirement. It is a threat of possible future legal action, and often an offer to avoid such action if the recipient does as the sender requests. The recipient can comply with the letter, wait for court action, or try to make some sort of compromise deal. Open source projects, as other answers suggest, often choose to comply.

Being or not being open source makes fairly little difference in trademark law.

If a commercial firm (Yoyodyne, say) had used the name "Portable Network Graphics" and the abbreviation "PNG" in trade, and taker such further straps as would be needed to protect it in the relevant countries, that firm would have a protectable trademark.

Note that is some countries, a trademark must be registered to have any protection at all (much of the EU follows this rule). In others, use in commerce can offer some protector even without registration (the US follows this rule).

Had this happened (in an alternate reality) Yoyodyne could have sent a cease and desist letter when open source developers started using the mark. If the devs did not cease, Yoyodyne might have obtained an injunction, or damages for trademark infringement, or both.

But had Yoyodyne failed to defend the mark effectively and allowed it to become generic, Yoyodyne might have lost all rights to it. Also, had Yoyodyne ceased to use it in trade for a significant period, they might have lost rights. This is a place where the different laws in different countries might lead to different results.

Note that "Portable Network Graphics" is rather descriptive, adn not particularly distinctive. Descriptive marks, like "Tasty Pizza" generally get weaker protection, while more distinctive marks, such as "LuAnn's Tastee Pizza" are more strongly protected, in general. Again this depends on the country, and the specific facts.

In general the first to use, or to register a mark, gets the rights. When one entity is the first to use, but a different one is first to register, things can get confusing, and results will be different in different countries.

Being or not being open source makes fairly little difference in trademark law.

If a commercial firm (Yoyodyne, say) had used the name "Portable Network Graphics" and the abbreviation "PNG" in trade, and taken such further steps as would be needed to protect it in the relevant countries, that firm would have a protectable trademark.

Note that is some countries, a trademark must be registered to have any protection at all (much of the EU follows this rule). In others, use in commerce can offer some protection even without registration (the US follows this rule).

Had this happened (in an alternate reality) Yoyodyne could have sent a cease and desist letter when open source developers started using the mark. If the devs did not cease, Yoyodyne might have obtained an injunction, or damages for trademark infringement, or both.

But had Yoyodyne failed to defend the mark effectively and allowed it to become generic, Yoyodyne might have lost all rights to it. Also, had Yoyodyne ceased to use it in trade for a significant period, they might have lost rights. This is a place where the different laws in different countries might lead to different results.

Note that "Portable Network Graphics" is rather descriptive, and not particularly distinctive. Descriptive marks, like "Tasty Pizza" generally get weaker protection, while more distinctive marks, such as "LuAnn's Tastee Pizza" are more strongly protected, in general. Again this depends on the country, and the specific facts.

In general the first to use, or to register a mark, gets the rights. When one entity is the first to use, but a different one is first to register, things can get confusing, and results will be different in different countries.