This appears to be an onslaught of wordplay.
The character's name is 丹生谷【にぶたに】 森夏【しんか】. Her given name is made up from two kanji, 森 and 夏 which both have more than one reading — a kun'yomi (kun reading) and an on'yomi (on reading).
- 森 "forest" has on'yomi しん and kun'yomi もり
- 夏 "summer" has on'yomi か and kun'yomi なつ
森夏 is also called モリサマ, which is a play on words (or rather play on readings) since 夏 would be "summer" in English, hence サマー in katakana, which is close to 様【さま】. Of course 様 is a polite honorific, whence 森夏 → もりサマー → モリサマ (森様) would be something like "Ms. Mori". (Of course 様 doesn't mean "Ms." in general.)
Now, her family name is 丹生谷【にぶたに】, which is quite a rare reading. The reading of the first kanji に is standard, but the second kanji 生 has a more standard reading せい. Putting them together gives にせい, which sounds like 偽【にせ】 "fake". Combining this with 夏 read サマー or サマ (= 様) we get that 丹生谷 森夏 → 丹生夏 → にせいサマー → ニセサマ (偽様) would be something like "Ms. Fake". Again, just like "Ms. Mori" it is a nickname derived from different readings of parts of her name.
Of course to say it just means "fake summer" is missing out on the wordplay, but this often happens in subtitles, which cannot translate such play on words (or play on readings).