Side note
See mishnayos Zevachim, 14:4-8, where different time periods are mentioned for when "במות" (altars outside of the Temple/Tabernacle) where permitted; you are correct in your assumption that they are currently forbidden (ibid., 8).

Real answer
The verse you cited in your question, according to Rashi (ibid.), refers to the Altar of the Tabernacle, which was made of packed dirt, with a plate copper exterior. More to the point, the last comment of Rashi on that verse explains that

בכל המקום אשר אזכיר את שמי. אשר אתן לך רשות להזכיר שם המפרש שלי, שם אבא אליך וברכתיך אשרה שכינתי עליך מכאן אתה למד שלא נתן רשות להזכיר שם המפרש אלא במקום שהשכינה באה שם, וזהו בית הבחירה שם נתן רשות לכהנים להזכיר שם המפרש בנשיאת כפים לברך את העם

 

Wherever I allow My name to be mentioned: [this means any place where] I allow my "שם המפרש" to be mentioned, to that place "I will come to you and bless you," [...]. From here we learn that the שם המפרש is only allowed to be mentioned in a place where the Shechinah comes to, which is the Temple; there the Kohanim were permitted to use the שם המפרש when they bless the people with the Priestly Blessing.

(translation my own)

Side note
See mishnayos Zevachim, 14:4-8, where different time periods are mentioned for when "במות" (altars outside of the Temple/Tabernacle) where permitted; you are correct in your assumption that they are currently forbidden (ibid., 8).

Real answer
The verse you cited in your question, according to Rashi (ibid.), refers to the Altar of the Tabernacle, which was made of packed dirt, with a plate copper exterior. More to the point, the last comment of Rashi on that verse explains that

בכל המקום אשר אזכיר את שמי. אשר אתן לך רשות להזכיר שם המפרש שלי, שם אבא אליך וברכתיך אשרה שכינתי עליך מכאן אתה למד שלא נתן רשות להזכיר שם המפרש אלא במקום שהשכינה באה שם, וזהו בית הבחירה שם נתן רשות לכהנים להזכיר שם המפרש בנשיאת כפים לברך את העם

Wherever I allow My name to be mentioned: [this means any place where] I allow my "שם המפרש" to be mentioned, to that place "I will come to you and bless you," [...]. From here we learn that the שם המפרש is only allowed to be mentioned in a place where the Shechinah comes to, which is the Temple; there the Kohanim were permitted to use the שם המפרש when they bless the people with the Priestly Blessing.

(translation my own)

See mishnayos Zevachim, 14:4-8, where different time periods are mentioned for when "במות" (altars outside of the Temple/Tabernacle) where permitted; you are correct in your assumption that they are currently forbidden (ibid., 8).

I don't have a source for you at the moment, but I believe that the verse you cited in your question refers to the Altar of the Tabernacle, which was made of packed dirt, with a plate copper exterior.

Side note
See mishnayos Zevachim, 14:4-8, where different time periods are mentioned for when "במות" (altars outside of the Temple/Tabernacle) where permitted; you are correct in your assumption that they are currently forbidden (ibid., 8).

Real answer
The verse you cited in your question, according to Rashi (ibid.), refers to the Altar of the Tabernacle, which was made of packed dirt, with a plate copper exterior. More to the point, the last comment of Rashi on that verse explains that

בכל המקום אשר אזכיר את שמי. אשר אתן לך רשות להזכיר שם המפרש שלי, שם אבא אליך וברכתיך אשרה שכינתי עליך מכאן אתה למד שלא נתן רשות להזכיר שם המפרש אלא במקום שהשכינה באה שם, וזהו בית הבחירה שם נתן רשות לכהנים להזכיר שם המפרש בנשיאת כפים לברך את העם

Wherever I allow My name to be mentioned: [this means any place where] I allow my "שם המפרש" to be mentioned, to that place "I will come to you and bless you," [...]. From here we learn that the שם המפרש is only allowed to be mentioned in a place where the Shechinah comes to, which is the Temple; there the Kohanim were permitted to use the שם המפרש when they bless the people with the Priestly Blessing.

(translation my own)